id	sid	tid	token	lemma	pos
ejpam-3422	1	1	european	european	PROPN
ejpam-3422	1	2	journal	journal	PROPN
ejpam-3422	1	3	of	of	ADP
ejpam-3422	1	4	pure	pure	ADJ
ejpam-3422	1	5	and	and	CCONJ
ejpam-3422	1	6	applied	apply	VERB
ejpam-3422	1	7	mathematics	mathematic	NOUN
ejpam-3422	1	8	vol	vol	NOUN
ejpam-3422	1	9	.	.	PROPN
ejpam-3422	2	1	12	12	NUM
ejpam-3422	2	2	,	,	PUNCT
ejpam-3422	2	3	no	no	INTJ
ejpam-3422	2	4	.	.	NOUN
ejpam-3422	2	5	2	2	NUM
ejpam-3422	2	6	,	,	PUNCT
ejpam-3422	2	7	2019	2019	NUM
ejpam-3422	2	8	,	,	PUNCT
ejpam-3422	2	9	409	409	NUM
ejpam-3422	2	10	-	-	SYM
ejpam-3422	2	11	417	417	NUM
ejpam-3422	2	12	issn	issn	PROPN
ejpam-3422	2	13	1307	1307	NUM
ejpam-3422	2	14	-	-	SYM
ejpam-3422	2	15	5543	5543	NUM
ejpam-3422	2	16	–	–	PUNCT
ejpam-3422	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3422	2	18	published	publish	VERB
ejpam-3422	2	19	by	by	ADP
ejpam-3422	2	20	new	new	PROPN
ejpam-3422	2	21	york	york	PROPN
ejpam-3422	2	22	business	business	PROPN
ejpam-3422	2	23	global	global	PROPN
ejpam-3422	2	24	some	some	DET
ejpam-3422	2	25	results	result	NOUN
ejpam-3422	2	26	on	on	ADP
ejpam-3422	2	27	fuzzy	fuzzy	ADJ
ejpam-3422	2	28	implicative	implicative	ADJ
ejpam-3422	2	29	hyper	hyper	ADJ
ejpam-3422	2	30	gr	gr	NOUN
ejpam-3422	2	31	-	-	PUNCT
ejpam-3422	2	32	ideals	ideal	NOUN
ejpam-3422	2	33	amila	amila	NOUN
ejpam-3422	2	34	p.	p.	NOUN
ejpam-3422	2	35	macodi	macodi	PROPN
ejpam-3422	2	36	-	-	PUNCT
ejpam-3422	2	37	ringia1,∗	ringia1,∗	NOUN
ejpam-3422	2	38	,	,	PUNCT
ejpam-3422	2	39	gaudencio	gaudencio	PROPN
ejpam-3422	2	40	c.	c.	PROPN
ejpam-3422	2	41	petalcorin	petalcorin	PROPN
ejpam-3422	2	42	,	,	PUNCT
ejpam-3422	2	43	jr.2	jr.2	PROPN
ejpam-3422	2	44	1	1	NUM
ejpam-3422	2	45	mathematics	mathematics	PROPN
ejpam-3422	2	46	department	department	NOUN
ejpam-3422	2	47	,	,	PUNCT
ejpam-3422	2	48	faculty	faculty	NOUN
ejpam-3422	2	49	,	,	PUNCT
ejpam-3422	2	50	mindanao	mindanao	PROPN
ejpam-3422	2	51	state	state	PROPN
ejpam-3422	2	52	university	university	PROPN
ejpam-3422	2	53	main	main	ADJ
ejpam-3422	2	54	campus	campus	NOUN
ejpam-3422	2	55	,	,	PUNCT
ejpam-3422	2	56	marawi	marawi	PROPN
ejpam-3422	2	57	city	city	PROPN
ejpam-3422	2	58	,	,	PUNCT
ejpam-3422	2	59	philippines	philippines	PROPN
ejpam-3422	2	60	2	2	NUM
ejpam-3422	2	61	department	department	NOUN
ejpam-3422	2	62	of	of	ADP
ejpam-3422	2	63	mathematics	mathematic	NOUN
ejpam-3422	2	64	and	and	CCONJ
ejpam-3422	2	65	statistics	statistic	NOUN
ejpam-3422	2	66	,	,	PUNCT
ejpam-3422	2	67	faculty	faculty	NOUN
ejpam-3422	2	68	,	,	PUNCT
ejpam-3422	2	69	msu	msu	PROPN
ejpam-3422	2	70	-	-	PUNCT
ejpam-3422	2	71	iligan	iligan	PROPN
ejpam-3422	2	72	institute	institute	PROPN
ejpam-3422	2	73	of	of	ADP
ejpam-3422	2	74	technology	technology	PROPN
ejpam-3422	2	75	,	,	PUNCT
ejpam-3422	2	76	iligan	iligan	PROPN
ejpam-3422	2	77	city	city	PROPN
ejpam-3422	2	78	,	,	PUNCT
ejpam-3422	3	1	philippines	philippine	NOUN
ejpam-3422	3	2	abstract	abstract	ADJ
ejpam-3422	3	3	.	.	PUNCT
ejpam-3422	4	1	the	the	DET
ejpam-3422	4	2	implicative	implicative	ADJ
ejpam-3422	4	3	hyper	hyper	ADJ
ejpam-3422	4	4	gr	gr	NOUN
ejpam-3422	4	5	-	-	PUNCT
ejpam-3422	4	6	ideals	ideal	NOUN
ejpam-3422	4	7	,	,	PUNCT
ejpam-3422	4	8	the	the	DET
ejpam-3422	4	9	fuzzy	fuzzy	ADJ
ejpam-3422	4	10	implicative	implicative	ADJ
ejpam-3422	4	11	hyper	hyper	ADJ
ejpam-3422	4	12	gr	gr	NOUN
ejpam-3422	4	13	-	-	PUNCT
ejpam-3422	4	14	ideals	ideal	NOUN
ejpam-3422	4	15	of	of	ADP
ejpam-3422	4	16	type	type	NOUN
ejpam-3422	4	17	1	1	NUM
ejpam-3422	4	18	and	and	CCONJ
ejpam-3422	4	19	the	the	DET
ejpam-3422	4	20	fuzzy	fuzzy	ADJ
ejpam-3422	4	21	implicative	implicative	ADJ
ejpam-3422	4	22	hyper	hyper	ADJ
ejpam-3422	4	23	gr	gr	NOUN
ejpam-3422	4	24	-	-	PUNCT
ejpam-3422	4	25	ideals	ideal	NOUN
ejpam-3422	4	26	of	of	ADP
ejpam-3422	4	27	type	type	NOUN
ejpam-3422	4	28	2	2	NUM
ejpam-3422	4	29	are	be	AUX
ejpam-3422	4	30	introduced	introduce	VERB
ejpam-3422	4	31	,	,	PUNCT
ejpam-3422	4	32	and	and	CCONJ
ejpam-3422	4	33	several	several	ADJ
ejpam-3422	4	34	properties	property	NOUN
ejpam-3422	4	35	are	be	AUX
ejpam-3422	4	36	investigated	investigate	VERB
ejpam-3422	4	37	.	.	PUNCT
ejpam-3422	5	1	characterizations	characterization	NOUN
ejpam-3422	5	2	of	of	ADP
ejpam-3422	5	3	fuzzy	fuzzy	ADJ
ejpam-3422	5	4	implicative	implicative	ADJ
ejpam-3422	5	5	hyper	hyper	ADJ
ejpam-3422	5	6	gr	gr	NOUN
ejpam-3422	5	7	-	-	PUNCT
ejpam-3422	5	8	ideals	ideal	NOUN
ejpam-3422	5	9	of	of	ADP
ejpam-3422	5	10	type	type	NOUN
ejpam-3422	5	11	1	1	NUM
ejpam-3422	5	12	are	be	AUX
ejpam-3422	5	13	established	establish	VERB
ejpam-3422	5	14	using	use	VERB
ejpam-3422	5	15	level	level	NOUN
ejpam-3422	5	16	subsets	subset	NOUN
ejpam-3422	5	17	of	of	ADP
ejpam-3422	5	18	fuzzy	fuzzy	ADJ
ejpam-3422	5	19	sets	set	NOUN
ejpam-3422	5	20	.	.	PUNCT
ejpam-3422	6	1	2010	2010	NUM
ejpam-3422	6	2	mathematics	mathematic	NOUN
ejpam-3422	6	3	subject	subject	NOUN
ejpam-3422	6	4	classifications	classification	NOUN
ejpam-3422	6	5	:	:	PUNCT
ejpam-3422	6	6	20n20	20n20	NUM
ejpam-3422	6	7	,	,	PUNCT
ejpam-3422	6	8	06f3	06f3	NUM
ejpam-3422	6	9	,	,	PUNCT
ejpam-3422	6	10	03g25	03g25	NOUN
ejpam-3422	6	11	,	,	PUNCT
ejpam-3422	6	12	03e72	03e72	NUM
ejpam-3422	6	13	,	,	PUNCT
ejpam-3422	6	14	03b52	03b52	VERB
ejpam-3422	6	15	key	key	ADJ
ejpam-3422	6	16	words	word	NOUN
ejpam-3422	6	17	and	and	CCONJ
ejpam-3422	6	18	phrases	phrase	NOUN
ejpam-3422	6	19	:	:	PUNCT
ejpam-3422	6	20	implicative	implicative	ADJ
ejpam-3422	6	21	hyper	hyper	ADJ
ejpam-3422	6	22	gr	gr	NOUN
ejpam-3422	6	23	-	-	PUNCT
ejpam-3422	6	24	ideals	ideal	NOUN
ejpam-3422	6	25	,	,	PUNCT
ejpam-3422	6	26	fuzzy	fuzzy	ADJ
ejpam-3422	6	27	implicative	implicative	ADJ
ejpam-3422	6	28	hyper	hyper	ADJ
ejpam-3422	6	29	gr	gr	NOUN
ejpam-3422	6	30	-	-	PUNCT
ejpam-3422	6	31	ideals	ideal	NOUN
ejpam-3422	6	32	of	of	ADP
ejpam-3422	6	33	type	type	NOUN
ejpam-3422	6	34	1	1	NUM
ejpam-3422	6	35	,	,	PUNCT
ejpam-3422	6	36	fuzzy	fuzzy	ADJ
ejpam-3422	6	37	implicative	implicative	ADJ
ejpam-3422	6	38	hyper	hyper	ADJ
ejpam-3422	6	39	gr	gr	NOUN
ejpam-3422	6	40	-	-	PUNCT
ejpam-3422	6	41	ideals	ideal	NOUN
ejpam-3422	6	42	of	of	ADP
ejpam-3422	6	43	type	type	NOUN
ejpam-3422	6	44	2	2	NUM
ejpam-3422	6	45	1	1	NUM
ejpam-3422	6	46	.	.	PUNCT
ejpam-3422	7	1	introduction	introduction	NOUN
ejpam-3422	7	2	hyperstructure	hyperstructure	PROPN
ejpam-3422	7	3	theory	theory	NOUN
ejpam-3422	7	4	was	be	AUX
ejpam-3422	7	5	introduced	introduce	VERB
ejpam-3422	7	6	in	in	ADP
ejpam-3422	7	7	1934	1934	NUM
ejpam-3422	7	8	by	by	ADP
ejpam-3422	7	9	f.	f.	PROPN
ejpam-3422	7	10	marty	marty	PROPN
ejpam-3422	8	1	[	[	X
ejpam-3422	8	2	11	11	NUM
ejpam-3422	8	3	]	]	PUNCT
ejpam-3422	8	4	at	at	ADP
ejpam-3422	8	5	the	the	DET
ejpam-3422	8	6	8th	8th	ADJ
ejpam-3422	8	7	congress	congress	PROPN
ejpam-3422	8	8	of	of	ADP
ejpam-3422	8	9	scandinavian	scandinavian	ADJ
ejpam-3422	8	10	mathematics	mathematic	NOUN
ejpam-3422	8	11	.	.	PUNCT
ejpam-3422	9	1	it	it	PRON
ejpam-3422	9	2	is	be	AUX
ejpam-3422	9	3	studied	study	VERB
ejpam-3422	9	4	from	from	ADP
ejpam-3422	9	5	the	the	DET
ejpam-3422	9	6	theoritical	theoritical	ADJ
ejpam-3422	9	7	point	point	NOUN
ejpam-3422	9	8	of	of	ADP
ejpam-3422	9	9	view	view	NOUN
ejpam-3422	9	10	and	and	CCONJ
ejpam-3422	9	11	for	for	ADP
ejpam-3422	9	12	their	their	PRON
ejpam-3422	9	13	applications	application	NOUN
ejpam-3422	9	14	to	to	ADP
ejpam-3422	9	15	many	many	ADJ
ejpam-3422	9	16	areas	area	NOUN
ejpam-3422	9	17	of	of	ADP
ejpam-3422	9	18	pure	pure	ADJ
ejpam-3422	9	19	and	and	CCONJ
ejpam-3422	9	20	applied	applied	ADJ
ejpam-3422	9	21	mathematics	mathematic	NOUN
ejpam-3422	9	22	.	.	PUNCT
ejpam-3422	10	1	y.b	y.b	PROPN
ejpam-3422	10	2	.	.	PROPN
ejpam-3422	10	3	jun	jun	PROPN
ejpam-3422	10	4	et	et	PROPN
ejpam-3422	10	5	al	al	PROPN
ejpam-3422	10	6	.	.	PROPN
ejpam-3422	10	7	applied	apply	VERB
ejpam-3422	10	8	this	this	DET
ejpam-3422	10	9	concept	concept	NOUN
ejpam-3422	10	10	to	to	PART
ejpam-3422	10	11	bck	bck	VERB
ejpam-3422	10	12	-	-	PUNCT
ejpam-3422	10	13	algebras	algebras	NOUN
ejpam-3422	11	1	[	[	X
ejpam-3422	11	2	8	8	NUM
ejpam-3422	11	3	]	]	PUNCT
ejpam-3422	11	4	and	and	CCONJ
ejpam-3422	11	5	x.x	x.x	PROPN
ejpam-3422	11	6	.	.	PROPN
ejpam-3422	11	7	long	long	PROPN
ejpam-3422	11	8	introduced	introduce	VERB
ejpam-3422	11	9	hyper	hyper	ADJ
ejpam-3422	11	10	bci	bci	NOUN
ejpam-3422	11	11	-	-	PUNCT
ejpam-3422	11	12	algebras	algebras	X
ejpam-3422	12	1	[	[	X
ejpam-3422	12	2	10	10	NUM
ejpam-3422	12	3	]	]	PUNCT
ejpam-3422	12	4	as	as	ADP
ejpam-3422	12	5	a	a	DET
ejpam-3422	12	6	generalization	generalization	NOUN
ejpam-3422	12	7	of	of	ADP
ejpam-3422	12	8	bci	bci	PROPN
ejpam-3422	12	9	-	-	PUNCT
ejpam-3422	12	10	algebras	algebra	NOUN
ejpam-3422	12	11	.	.	PUNCT
ejpam-3422	13	1	different	different	ADJ
ejpam-3422	13	2	types	type	NOUN
ejpam-3422	13	3	of	of	ADP
ejpam-3422	13	4	hyper	hyper	ADJ
ejpam-3422	13	5	bci	bci	NOUN
ejpam-3422	13	6	-	-	PUNCT
ejpam-3422	13	7	ideals	ideal	NOUN
ejpam-3422	13	8	are	be	AUX
ejpam-3422	13	9	also	also	ADV
ejpam-3422	13	10	defined	define	VERB
ejpam-3422	13	11	in	in	ADP
ejpam-3422	13	12	[	[	X
ejpam-3422	13	13	10	10	NUM
ejpam-3422	13	14	]	]	PUNCT
ejpam-3422	13	15	.	.	PUNCT
ejpam-3422	14	1	after	after	ADP
ejpam-3422	14	2	the	the	DET
ejpam-3422	14	3	introduction	introduction	NOUN
ejpam-3422	14	4	of	of	ADP
ejpam-3422	14	5	the	the	DET
ejpam-3422	14	6	concept	concept	NOUN
ejpam-3422	14	7	of	of	ADP
ejpam-3422	14	8	hyper	hyper	ADJ
ejpam-3422	14	9	bci	bci	NOUN
ejpam-3422	14	10	-	-	PUNCT
ejpam-3422	14	11	algebras	algebra	NOUN
ejpam-3422	14	12	,	,	PUNCT
ejpam-3422	14	13	several	several	ADJ
ejpam-3422	14	14	researches	research	NOUN
ejpam-3422	14	15	were	be	AUX
ejpam-3422	14	16	conducted	conduct	VERB
ejpam-3422	14	17	.	.	PUNCT
ejpam-3422	15	1	among	among	ADP
ejpam-3422	15	2	these	these	DET
ejpam-3422	15	3	studies	study	NOUN
ejpam-3422	15	4	are	be	AUX
ejpam-3422	15	5	fuzzy	fuzzy	ADJ
ejpam-3422	15	6	hyper	hyper	ADJ
ejpam-3422	15	7	bck	bck	NOUN
ejpam-3422	15	8	-	-	PUNCT
ejpam-3422	15	9	ideals	ideal	NOUN
ejpam-3422	15	10	of	of	ADP
ejpam-3422	15	11	hyper	hyper	ADJ
ejpam-3422	15	12	bck	bck	NOUN
ejpam-3422	15	13	-	-	PUNCT
ejpam-3422	15	14	algebras	algebras	X
ejpam-3422	15	15	[	[	X
ejpam-3422	15	16	6	6	NUM
ejpam-3422	15	17	]	]	PUNCT
ejpam-3422	15	18	,	,	PUNCT
ejpam-3422	15	19	fuzzy	fuzzy	ADJ
ejpam-3422	15	20	ideals	ideal	NOUN
ejpam-3422	15	21	in	in	ADP
ejpam-3422	15	22	hyper	hyper	ADJ
ejpam-3422	15	23	bci	bci	NOUN
ejpam-3422	15	24	-	-	PUNCT
ejpam-3422	15	25	algebras	algebras	X
ejpam-3422	15	26	[	[	X
ejpam-3422	15	27	13	13	NUM
ejpam-3422	15	28	]	]	PUNCT
ejpam-3422	15	29	,	,	PUNCT
ejpam-3422	15	30	fuzzy	fuzzy	ADJ
ejpam-3422	15	31	implicative	implicative	ADJ
ejpam-3422	15	32	hyper	hyper	ADJ
ejpam-3422	15	33	bck	bck	NOUN
ejpam-3422	15	34	-	-	PUNCT
ejpam-3422	15	35	ideals	ideal	NOUN
ejpam-3422	15	36	of	of	ADP
ejpam-3422	15	37	hyper	hyper	ADJ
ejpam-3422	15	38	bck	bck	NOUN
ejpam-3422	15	39	-	-	PUNCT
ejpam-3422	15	40	algebras	algebras	X
ejpam-3422	16	1	[	[	X
ejpam-3422	16	2	7	7	NUM
ejpam-3422	16	3	]	]	PUNCT
ejpam-3422	16	4	,	,	PUNCT
ejpam-3422	16	5	bi	bi	ADJ
ejpam-3422	16	6	-	-	ADJ
ejpam-3422	16	7	polar	polar	ADV
ejpam-3422	16	8	-	-	PUNCT
ejpam-3422	16	9	valued	value	VERB
ejpam-3422	16	10	fuzzy	fuzzy	ADJ
ejpam-3422	16	11	hyper	hyper	ADJ
ejpam-3422	16	12	subalgebras	subalgebra	NOUN
ejpam-3422	16	13	of	of	ADP
ejpam-3422	16	14	a	a	DET
ejpam-3422	16	15	hyper	hyper	ADJ
ejpam-3422	16	16	bci	bci	NOUN
ejpam-3422	16	17	-	-	NOUN
ejpam-3422	16	18	algebra	algebra	NOUN
ejpam-3422	16	19	[	[	X
ejpam-3422	16	20	12	12	NUM
ejpam-3422	16	21	]	]	PUNCT
ejpam-3422	16	22	,	,	PUNCT
ejpam-3422	16	23	intuitionistic	intuitionistic	ADJ
ejpam-3422	16	24	fuzzy	fuzzy	ADJ
ejpam-3422	16	25	hyper	hyper	ADJ
ejpam-3422	16	26	bck	bck	NOUN
ejpam-3422	16	27	-	-	PUNCT
ejpam-3422	16	28	ideals	ideal	NOUN
ejpam-3422	16	29	of	of	ADP
ejpam-3422	16	30	hyper	hyper	ADJ
ejpam-3422	16	31	bck	bck	NOUN
ejpam-3422	16	32	-	-	PUNCT
ejpam-3422	16	33	algebras	algebras	X
ejpam-3422	17	1	[	[	X
ejpam-3422	17	2	2	2	NUM
ejpam-3422	17	3	]	]	PUNCT
ejpam-3422	17	4	,	,	PUNCT
ejpam-3422	17	5	and	and	CCONJ
ejpam-3422	17	6	intuitionistic	intuitionistic	ADJ
ejpam-3422	17	7	fuzzy	fuzzy	ADJ
ejpam-3422	17	8	ideals	ideal	NOUN
ejpam-3422	17	9	in	in	ADP
ejpam-3422	17	10	hyper	hyper	ADJ
ejpam-3422	17	11	bci	bci	NOUN
ejpam-3422	17	12	-	-	PUNCT
ejpam-3422	17	13	algebras	algebras	X
ejpam-3422	18	1	[	[	X
ejpam-3422	18	2	14	14	NUM
ejpam-3422	18	3	]	]	PUNCT
ejpam-3422	18	4	where	where	SCONJ
ejpam-3422	18	5	fuzzy	fuzzy	ADJ
ejpam-3422	18	6	sets	set	NOUN
ejpam-3422	18	7	are	be	AUX
ejpam-3422	18	8	applied	apply	VERB
ejpam-3422	18	9	to	to	ADP
ejpam-3422	18	10	hyper	hyper	ADJ
ejpam-3422	18	11	bck	bck	NOUN
ejpam-3422	18	12	-	-	PUNCT
ejpam-3422	18	13	algebras	algebra	NOUN
ejpam-3422	18	14	and	and	CCONJ
ejpam-3422	18	15	hyper	hyper	ADJ
ejpam-3422	18	16	bci	bci	NOUN
ejpam-3422	18	17	-	-	PUNCT
ejpam-3422	18	18	algebras	algebra	NOUN
ejpam-3422	18	19	.	.	PUNCT
ejpam-3422	19	1	by	by	ADP
ejpam-3422	19	2	following	follow	VERB
ejpam-3422	19	3	these	these	DET
ejpam-3422	19	4	hyperstructures	hyperstructure	NOUN
ejpam-3422	19	5	,	,	PUNCT
ejpam-3422	19	6	indangan	indangan	PROPN
ejpam-3422	19	7	et	et	PROPN
ejpam-3422	19	8	al	al	PROPN
ejpam-3422	19	9	.	.	PROPN
ejpam-3422	19	10	introduced	introduce	VERB
ejpam-3422	19	11	hyper	hyper	ADJ
ejpam-3422	19	12	gr	gr	NOUN
ejpam-3422	19	13	-	-	PUNCT
ejpam-3422	19	14	algebras	algebras	NOUN
ejpam-3422	20	1	[	[	X
ejpam-3422	20	2	4	4	NUM
ejpam-3422	20	3	]	]	PUNCT
ejpam-3422	20	4	.	.	PUNCT
ejpam-3422	21	1	they	they	PRON
ejpam-3422	21	2	established	establish	VERB
ejpam-3422	21	3	some	some	DET
ejpam-3422	21	4	results	result	NOUN
ejpam-3422	21	5	on	on	ADP
ejpam-3422	21	6	hyper	hyper	ADJ
ejpam-3422	21	7	gr	gr	NOUN
ejpam-3422	21	8	-	-	PUNCT
ejpam-3422	21	9	ideals	ideal	NOUN
ejpam-3422	21	10	and	and	CCONJ
ejpam-3422	21	11	hyper	hyper	ADJ
ejpam-3422	21	12	homomorphic	homomorphic	ADJ
ejpam-3422	21	13	properties	property	NOUN
ejpam-3422	21	14	on	on	ADP
ejpam-3422	21	15	hyper	hyper	ADJ
ejpam-3422	21	16	gr	gr	NOUN
ejpam-3422	21	17	-	-	PUNCT
ejpam-3422	21	18	algebras	algebras	NOUN
ejpam-3422	22	1	[	[	X
ejpam-3422	22	2	5	5	NUM
ejpam-3422	22	3	]	]	PUNCT
ejpam-3422	22	4	.	.	PUNCT
ejpam-3422	22	5	fuzzy	fuzzy	ADJ
ejpam-3422	22	6	set	set	PROPN
ejpam-3422	22	7	was	be	AUX
ejpam-3422	22	8	introduced	introduce	VERB
ejpam-3422	22	9	by	by	ADP
ejpam-3422	22	10	l.a	l.a	PROPN
ejpam-3422	22	11	.	.	PROPN
ejpam-3422	22	12	zadeh	zadeh	PROPN
ejpam-3422	23	1	[	[	X
ejpam-3422	23	2	17	17	NUM
ejpam-3422	23	3	]	]	PUNCT
ejpam-3422	23	4	.	.	PUNCT
ejpam-3422	24	1	this	this	DET
ejpam-3422	24	2	concept	concept	NOUN
ejpam-3422	24	3	of	of	ADP
ejpam-3422	24	4	fuzzy	fuzzy	ADJ
ejpam-3422	24	5	sets	set	NOUN
ejpam-3422	24	6	are	be	AUX
ejpam-3422	24	7	extremely	extremely	ADV
ejpam-3422	24	8	useful	useful	ADJ
ejpam-3422	24	9	for	for	ADP
ejpam-3422	24	10	many	many	ADJ
ejpam-3422	24	11	people	people	NOUN
ejpam-3422	24	12	involved	involve	VERB
ejpam-3422	24	13	in	in	ADP
ejpam-3422	24	14	research	research	NOUN
ejpam-3422	24	15	and	and	CCONJ
ejpam-3422	24	16	∗corresponding	∗corresponde	VERB
ejpam-3422	24	17	author	author	NOUN
ejpam-3422	24	18	.	.	PUNCT
ejpam-3422	25	1	doi	doi	NOUN
ejpam-3422	25	2	:	:	PUNCT
ejpam-3422	25	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3422	https://doi.org/10.29020/nybg.ejpam.v12i2.3422	NOUN
ejpam-3422	25	4	email	email	NOUN
ejpam-3422	25	5	addresses	address	NOUN
ejpam-3422	25	6	:	:	PUNCT
ejpam-3422	25	7	amila.macodi-ringia@g.msuiit.edu.ph	amila.macodi-ringia@g.msuiit.edu.ph	PROPN
ejpam-3422	25	8	(	(	PUNCT
ejpam-3422	25	9	a.	a.	NOUN
ejpam-3422	25	10	macodi	macodi	NOUN
ejpam-3422	25	11	-	-	PUNCT
ejpam-3422	25	12	ringia	ringia	NOUN
ejpam-3422	25	13	)	)	PUNCT
ejpam-3422	25	14	,	,	PUNCT
ejpam-3422	25	15	gaudencio.petalcorin@g.msuiit.edu.ph	gaudencio.petalcorin@g.msuiit.edu.ph	PROPN
ejpam-3422	25	16	(	(	PUNCT
ejpam-3422	25	17	g.	g.	PROPN
ejpam-3422	25	18	petalcorin	petalcorin	PROPN
ejpam-3422	25	19	,	,	PUNCT
ejpam-3422	25	20	jr	jr	PROPN
ejpam-3422	25	21	.	.	PUNCT
ejpam-3422	25	22	)	)	PUNCT
ejpam-3422	25	23	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3422	26	1	409	409	NUM
ejpam-3422	26	2	©	©	PROPN
ejpam-3422	26	3	2019	2019	NUM
ejpam-3422	26	4	ejpam	ejpam	NOUN
ejpam-3422	26	5	all	all	DET
ejpam-3422	26	6	rights	right	NOUN
ejpam-3422	26	7	reserved	reserve	VERB
ejpam-3422	26	8	.	.	PUNCT
ejpam-3422	27	1	a.	a.	NOUN
ejpam-3422	27	2	macodi	macodi	PROPN
ejpam-3422	27	3	-	-	PUNCT
ejpam-3422	27	4	ringia	ringia	ADJ
ejpam-3422	27	5	,	,	PUNCT
ejpam-3422	27	6	g.	g.	PROPN
ejpam-3422	27	7	petalcorin	petalcorin	PROPN
ejpam-3422	27	8	,	,	PUNCT
ejpam-3422	27	9	jr	jr	PROPN
ejpam-3422	27	10	.	.	PROPN
ejpam-3422	27	11	/	/	SYM
ejpam-3422	27	12	eur	eur	PROPN
ejpam-3422	27	13	.	.	PUNCT
ejpam-3422	28	1	j.	j.	PROPN
ejpam-3422	28	2	pure	pure	PROPN
ejpam-3422	28	3	appl	appl	PROPN
ejpam-3422	28	4	.	.	PROPN
ejpam-3422	28	5	math	math	PROPN
ejpam-3422	28	6	,	,	PUNCT
ejpam-3422	28	7	12	12	NUM
ejpam-3422	28	8	(	(	PUNCT
ejpam-3422	28	9	2	2	NUM
ejpam-3422	28	10	)	)	PUNCT
ejpam-3422	28	11	(	(	PUNCT
ejpam-3422	28	12	2019	2019	NUM
ejpam-3422	28	13	)	)	PUNCT
ejpam-3422	28	14	,	,	PUNCT
ejpam-3422	28	15	409	409	NUM
ejpam-3422	28	16	-	-	SYM
ejpam-3422	28	17	417	417	NUM
ejpam-3422	28	18	410	410	NUM
ejpam-3422	28	19	development	development	NOUN
ejpam-3422	28	20	including	include	VERB
ejpam-3422	28	21	engineers	engineer	NOUN
ejpam-3422	28	22	,	,	PUNCT
ejpam-3422	28	23	mathematicians	mathematician	NOUN
ejpam-3422	28	24	,	,	PUNCT
ejpam-3422	28	25	computer	computer	NOUN
ejpam-3422	28	26	software	software	NOUN
ejpam-3422	28	27	developers	developer	NOUN
ejpam-3422	28	28	and	and	CCONJ
ejpam-3422	28	29	researchers	researcher	NOUN
ejpam-3422	28	30	,	,	PUNCT
ejpam-3422	28	31	natural	natural	ADJ
ejpam-3422	28	32	scientists	scientist	NOUN
ejpam-3422	28	33	,	,	PUNCT
ejpam-3422	28	34	medical	medical	ADJ
ejpam-3422	28	35	researchers	researcher	NOUN
ejpam-3422	28	36	,	,	PUNCT
ejpam-3422	28	37	social	social	ADJ
ejpam-3422	28	38	scientists	scientist	NOUN
ejpam-3422	28	39	,	,	PUNCT
ejpam-3422	28	40	public	public	ADJ
ejpam-3422	28	41	policy	policy	NOUN
ejpam-3422	28	42	analysts	analyst	NOUN
ejpam-3422	28	43	,	,	PUNCT
ejpam-3422	28	44	business	business	NOUN
ejpam-3422	28	45	analysts	analyst	NOUN
ejpam-3422	28	46	,	,	PUNCT
ejpam-3422	28	47	and	and	CCONJ
ejpam-3422	28	48	jurists	jurist	NOUN
ejpam-3422	28	49	[	[	X
ejpam-3422	28	50	15	15	NUM
ejpam-3422	28	51	]	]	PUNCT
ejpam-3422	28	52	.	.	PUNCT
ejpam-3422	29	1	with	with	ADP
ejpam-3422	29	2	this	this	PRON
ejpam-3422	29	3	,	,	PUNCT
ejpam-3422	29	4	several	several	ADJ
ejpam-3422	29	5	researches	research	NOUN
ejpam-3422	29	6	investigated	investigate	VERB
ejpam-3422	29	7	on	on	ADP
ejpam-3422	29	8	the	the	DET
ejpam-3422	29	9	generalization	generalization	NOUN
ejpam-3422	29	10	of	of	ADP
ejpam-3422	29	11	the	the	DET
ejpam-3422	29	12	notion	notion	NOUN
ejpam-3422	29	13	of	of	ADP
ejpam-3422	29	14	fuzzy	fuzzy	ADJ
ejpam-3422	29	15	sets	set	NOUN
ejpam-3422	29	16	.	.	PUNCT
ejpam-3422	30	1	other	other	ADJ
ejpam-3422	30	2	studies	study	NOUN
ejpam-3422	30	3	where	where	SCONJ
ejpam-3422	30	4	fuzzy	fuzzy	ADJ
ejpam-3422	30	5	sets	set	NOUN
ejpam-3422	30	6	are	be	AUX
ejpam-3422	30	7	applied	apply	VERB
ejpam-3422	30	8	are	be	AUX
ejpam-3422	30	9	hyper	hyper	ADJ
ejpam-3422	30	10	k	k	NOUN
ejpam-3422	30	11	-	-	PUNCT
ejpam-3422	30	12	subalgebras	subalgebras	PROPN
ejpam-3422	30	13	based	base	VERB
ejpam-3422	30	14	on	on	ADP
ejpam-3422	30	15	fuzzy	fuzzy	ADJ
ejpam-3422	30	16	points	point	NOUN
ejpam-3422	31	1	[	[	X
ejpam-3422	31	2	9	9	NUM
ejpam-3422	31	3	]	]	PUNCT
ejpam-3422	31	4	and	and	CCONJ
ejpam-3422	31	5	on	on	ADP
ejpam-3422	31	6	fuzzy	fuzzy	ADJ
ejpam-3422	31	7	hyper	hyper	ADJ
ejpam-3422	31	8	b	b	NOUN
ejpam-3422	31	9	-	-	PUNCT
ejpam-3422	31	10	ideals	ideal	NOUN
ejpam-3422	31	11	of	of	ADP
ejpam-3422	31	12	hyper	hyper	ADJ
ejpam-3422	31	13	b	b	NOUN
ejpam-3422	31	14	-	-	PUNCT
ejpam-3422	31	15	algebras	algebras	X
ejpam-3422	32	1	[	[	X
ejpam-3422	32	2	16	16	NUM
ejpam-3422	32	3	]	]	PUNCT
ejpam-3422	32	4	.	.	PUNCT
ejpam-3422	33	1	in	in	ADP
ejpam-3422	33	2	this	this	DET
ejpam-3422	33	3	paper	paper	NOUN
ejpam-3422	33	4	,	,	PUNCT
ejpam-3422	33	5	we	we	PRON
ejpam-3422	33	6	introduce	introduce	VERB
ejpam-3422	33	7	an	an	DET
ejpam-3422	33	8	implicative	implicative	ADJ
ejpam-3422	33	9	hyper	hyper	ADJ
ejpam-3422	33	10	gr	gr	NOUN
ejpam-3422	33	11	-	-	PUNCT
ejpam-3422	33	12	ideal	ideal	NOUN
ejpam-3422	33	13	and	and	CCONJ
ejpam-3422	33	14	apply	apply	VERB
ejpam-3422	33	15	fuzzy	fuzzy	ADJ
ejpam-3422	33	16	sets	set	NOUN
ejpam-3422	33	17	on	on	ADP
ejpam-3422	33	18	this	this	DET
ejpam-3422	33	19	notion	notion	NOUN
ejpam-3422	33	20	.	.	PUNCT
ejpam-3422	34	1	the	the	DET
ejpam-3422	34	2	definition	definition	NOUN
ejpam-3422	34	3	of	of	ADP
ejpam-3422	34	4	implicative	implicative	ADJ
ejpam-3422	34	5	hyper	hyper	ADJ
ejpam-3422	34	6	gr	gr	NOUN
ejpam-3422	34	7	-	-	PUNCT
ejpam-3422	34	8	ideal	ideal	NOUN
ejpam-3422	34	9	is	be	AUX
ejpam-3422	34	10	somewhat	somewhat	ADV
ejpam-3422	34	11	alike	alike	ADV
ejpam-3422	34	12	with	with	ADP
ejpam-3422	34	13	the	the	DET
ejpam-3422	34	14	definition	definition	NOUN
ejpam-3422	34	15	of	of	ADP
ejpam-3422	34	16	weak	weak	ADJ
ejpam-3422	34	17	implicative	implicative	ADJ
ejpam-3422	34	18	hyper	hyper	ADJ
ejpam-3422	34	19	bck	bck	NOUN
ejpam-3422	34	20	-	-	PUNCT
ejpam-3422	34	21	ideal	ideal	NOUN
ejpam-3422	34	22	[	[	X
ejpam-3422	34	23	1	1	NUM
ejpam-3422	34	24	]	]	PUNCT
ejpam-3422	34	25	.	.	PUNCT
ejpam-3422	35	1	however	however	ADV
ejpam-3422	35	2	,	,	PUNCT
ejpam-3422	35	3	some	some	DET
ejpam-3422	35	4	examples	example	NOUN
ejpam-3422	35	5	in	in	ADP
ejpam-3422	35	6	section	section	NOUN
ejpam-3422	35	7	3	3	NUM
ejpam-3422	35	8	are	be	AUX
ejpam-3422	35	9	not	not	PART
ejpam-3422	35	10	hyper	hyper	ADJ
ejpam-3422	35	11	bci	bci	NOUN
ejpam-3422	35	12	-	-	PUNCT
ejpam-3422	35	13	algebras	algebras	X
ejpam-3422	35	14	.	.	PUNCT
ejpam-3422	36	1	these	these	DET
ejpam-3422	36	2	examples	example	NOUN
ejpam-3422	36	3	show	show	VERB
ejpam-3422	36	4	that	that	SCONJ
ejpam-3422	36	5	implicative	implicative	ADJ
ejpam-3422	36	6	hyper	hyper	ADJ
ejpam-3422	36	7	gr	gr	NOUN
ejpam-3422	36	8	-	-	PUNCT
ejpam-3422	36	9	ideals	ideal	NOUN
ejpam-3422	36	10	and	and	CCONJ
ejpam-3422	36	11	weak	weak	ADJ
ejpam-3422	36	12	implicative	implicative	ADJ
ejpam-3422	36	13	hyper	hyper	ADJ
ejpam-3422	36	14	bck	bck	NOUN
ejpam-3422	36	15	-	-	PUNCT
ejpam-3422	36	16	ideals	ideal	NOUN
ejpam-3422	36	17	are	be	AUX
ejpam-3422	36	18	not	not	PART
ejpam-3422	36	19	equivalent	equivalent	ADJ
ejpam-3422	36	20	.	.	PUNCT
ejpam-3422	37	1	other	other	ADJ
ejpam-3422	37	2	than	than	ADP
ejpam-3422	37	3	implicative	implicative	ADJ
ejpam-3422	37	4	hyper	hyper	ADJ
ejpam-3422	37	5	grideals	grideal	NOUN
ejpam-3422	37	6	,	,	PUNCT
ejpam-3422	37	7	two	two	NUM
ejpam-3422	37	8	types	type	NOUN
ejpam-3422	37	9	of	of	ADP
ejpam-3422	37	10	fuzzy	fuzzy	ADJ
ejpam-3422	37	11	implicative	implicative	ADJ
ejpam-3422	37	12	hyper	hyper	ADJ
ejpam-3422	37	13	gr	gr	NOUN
ejpam-3422	37	14	-	-	PUNCT
ejpam-3422	37	15	ideals	ideal	NOUN
ejpam-3422	37	16	are	be	AUX
ejpam-3422	37	17	introduced	introduce	VERB
ejpam-3422	37	18	and	and	CCONJ
ejpam-3422	37	19	investigated	investigate	VERB
ejpam-3422	37	20	.	.	PUNCT
ejpam-3422	38	1	using	use	VERB
ejpam-3422	38	2	the	the	DET
ejpam-3422	38	3	notion	notion	NOUN
ejpam-3422	38	4	of	of	ADP
ejpam-3422	38	5	level	level	NOUN
ejpam-3422	38	6	subsets	subset	NOUN
ejpam-3422	38	7	of	of	ADP
ejpam-3422	38	8	a	a	DET
ejpam-3422	38	9	fuzzy	fuzzy	ADJ
ejpam-3422	38	10	set	set	NOUN
ejpam-3422	38	11	,	,	PUNCT
ejpam-3422	38	12	we	we	PRON
ejpam-3422	38	13	give	give	VERB
ejpam-3422	38	14	a	a	DET
ejpam-3422	38	15	characterization	characterization	NOUN
ejpam-3422	38	16	of	of	ADP
ejpam-3422	38	17	a	a	DET
ejpam-3422	38	18	fuzzy	fuzzy	ADJ
ejpam-3422	38	19	implicative	implicative	ADJ
ejpam-3422	38	20	hyper	hyper	ADJ
ejpam-3422	38	21	gr	gr	NOUN
ejpam-3422	38	22	-	-	PUNCT
ejpam-3422	38	23	ideal	ideal	NOUN
ejpam-3422	38	24	of	of	ADP
ejpam-3422	38	25	type	type	NOUN
ejpam-3422	38	26	1	1	NUM
ejpam-3422	38	27	.	.	NOUN
ejpam-3422	38	28	2	2	NUM
ejpam-3422	38	29	.	.	X
ejpam-3422	38	30	preliminaries	preliminary	NOUN
ejpam-3422	38	31	let	let	VERB
ejpam-3422	38	32	p	p	PROPN
ejpam-3422	38	33	(	(	PUNCT
ejpam-3422	38	34	h	h	NOUN
ejpam-3422	38	35	)	)	PUNCT
ejpam-3422	38	36	be	be	VERB
ejpam-3422	38	37	the	the	DET
ejpam-3422	38	38	power	power	NOUN
ejpam-3422	38	39	set	set	NOUN
ejpam-3422	38	40	of	of	ADP
ejpam-3422	38	41	h.	h.	PROPN
ejpam-3422	38	42	consider	consider	VERB
ejpam-3422	38	43	p	p	PROPN
ejpam-3422	38	44	∗(h	∗(h	PROPN
ejpam-3422	38	45	)	)	PUNCT
ejpam-3422	39	1	=	=	SYM
ejpam-3422	39	2	p	p	X
ejpam-3422	39	3	(	(	PUNCT
ejpam-3422	39	4	h	h	NOUN
ejpam-3422	39	5	)	)	PUNCT
ejpam-3422	39	6	\	\	NOUN
ejpam-3422	39	7	{	{	PUNCT
ejpam-3422	39	8	φ	φ	NOUN
ejpam-3422	39	9	}	}	PUNCT
ejpam-3422	39	10	.	.	PUNCT
ejpam-3422	40	1	a	a	DET
ejpam-3422	40	2	hyperoperation	hyperoperation	NOUN
ejpam-3422	40	3	on	on	ADP
ejpam-3422	40	4	a	a	DET
ejpam-3422	40	5	nonempty	nonempty	ADV
ejpam-3422	40	6	set	set	VERB
ejpam-3422	40	7	h	h	NOUN
ejpam-3422	40	8	is	be	AUX
ejpam-3422	40	9	a	a	DET
ejpam-3422	40	10	function	function	NOUN
ejpam-3422	40	11	~	~	PUNCT
ejpam-3422	40	12	:	:	PUNCT
ejpam-3422	40	13	h	h	NOUN
ejpam-3422	40	14	×	×	NOUN
ejpam-3422	40	15	h	h	NOUN
ejpam-3422	40	16	→	→	SYM
ejpam-3422	40	17	p	p	PROPN
ejpam-3422	40	18	∗(h	∗(h	PROPN
ejpam-3422	40	19	)	)	PUNCT
ejpam-3422	40	20	.	.	PUNCT
ejpam-3422	41	1	the	the	DET
ejpam-3422	41	2	image	image	NOUN
ejpam-3422	41	3	of	of	ADP
ejpam-3422	41	4	(	(	PUNCT
ejpam-3422	41	5	x	x	NOUN
ejpam-3422	41	6	,	,	PUNCT
ejpam-3422	41	7	y	y	NOUN
ejpam-3422	41	8	)	)	PUNCT
ejpam-3422	41	9	∈	∈	PROPN
ejpam-3422	41	10	h	h	NOUN
ejpam-3422	41	11	×	×	NOUN
ejpam-3422	41	12	h	h	NOUN
ejpam-3422	41	13	under	under	ADP
ejpam-3422	41	14	~	~	PUNCT
ejpam-3422	41	15	is	be	AUX
ejpam-3422	41	16	denoted	denote	VERB
ejpam-3422	41	17	by	by	ADP
ejpam-3422	41	18	x	x	X
ejpam-3422	41	19	~	~	PUNCT
ejpam-3422	41	20	y.	y.	NOUN
ejpam-3422	41	21	if	if	SCONJ
ejpam-3422	41	22	x	x	SYM
ejpam-3422	41	23	∈	∈	PROPN
ejpam-3422	41	24	h	h	NOUN
ejpam-3422	41	25	and	and	CCONJ
ejpam-3422	41	26	a	a	DET
ejpam-3422	41	27	,	,	PUNCT
ejpam-3422	41	28	b	b	NOUN
ejpam-3422	41	29	are	be	AUX
ejpam-3422	41	30	nonempty	nonempty	ADJ
ejpam-3422	41	31	subsets	subset	NOUN
ejpam-3422	41	32	of	of	ADP
ejpam-3422	41	33	h	h	NOUN
ejpam-3422	41	34	,	,	PUNCT
ejpam-3422	41	35	then	then	ADV
ejpam-3422	41	36	we	we	PRON
ejpam-3422	41	37	define	define	VERB
ejpam-3422	41	38	a~	a~	PROPN
ejpam-3422	41	39	b	b	PROPN
ejpam-3422	41	40	=	=	PUNCT
ejpam-3422	41	41	⋃	⋃	NOUN
ejpam-3422	41	42	a∈a	a∈a	ADJ
ejpam-3422	41	43	,	,	PUNCT
ejpam-3422	41	44	b∈b	b∈b	NOUN
ejpam-3422	41	45	a~	a~	PROPN
ejpam-3422	41	46	b	b	PROPN
ejpam-3422	41	47	;	;	PUNCT
ejpam-3422	42	1	a~	a~	PROPN
ejpam-3422	42	2	x	x	SYM
ejpam-3422	42	3	=	=	SYM
ejpam-3422	42	4	a~	a~	PROPN
ejpam-3422	42	5	{	{	PUNCT
ejpam-3422	42	6	x	x	NOUN
ejpam-3422	42	7	}	}	PUNCT
ejpam-3422	42	8	;	;	PUNCT
ejpam-3422	42	9	and	and	CCONJ
ejpam-3422	42	10	x~	x~	PROPN
ejpam-3422	42	11	b	b	X
ejpam-3422	42	12	=	=	PRON
ejpam-3422	42	13	{	{	PUNCT
ejpam-3422	42	14	x}~	x}~	PROPN
ejpam-3422	42	15	b.	b.	PROPN
ejpam-3422	42	16	moreover	moreover	ADV
ejpam-3422	42	17	,	,	PUNCT
ejpam-3422	42	18	x	x	X
ejpam-3422	42	19	�	�	PROPN
ejpam-3422	42	20	y	y	PROPN
ejpam-3422	42	21	if	if	SCONJ
ejpam-3422	42	22	and	and	CCONJ
ejpam-3422	42	23	only	only	ADV
ejpam-3422	42	24	if	if	SCONJ
ejpam-3422	42	25	0	0	NUM
ejpam-3422	42	26	∈	∈	PROPN
ejpam-3422	42	27	x~	x~	NUM
ejpam-3422	42	28	y	y	PROPN
ejpam-3422	42	29	;	;	PUNCT
ejpam-3422	42	30	and	and	CCONJ
ejpam-3422	42	31	a	a	DET
ejpam-3422	42	32	�	�	PROPN
ejpam-3422	42	33	b	b	PROPN
ejpam-3422	42	34	if	if	SCONJ
ejpam-3422	43	1	and	and	CCONJ
ejpam-3422	43	2	only	only	ADV
ejpam-3422	43	3	if	if	SCONJ
ejpam-3422	43	4	for	for	ADP
ejpam-3422	43	5	any	any	DET
ejpam-3422	43	6	a	a	DET
ejpam-3422	43	7	∈	∈	PROPN
ejpam-3422	43	8	a	a	PRON
ejpam-3422	43	9	,	,	PUNCT
ejpam-3422	43	10	there	there	PRON
ejpam-3422	43	11	exists	exist	VERB
ejpam-3422	43	12	b	b	PROPN
ejpam-3422	43	13	∈	∈	PROPN
ejpam-3422	43	14	b	b	NOUN
ejpam-3422	43	15	such	such	ADJ
ejpam-3422	43	16	that	that	SCONJ
ejpam-3422	43	17	a	a	DET
ejpam-3422	43	18	�	�	PROPN
ejpam-3422	43	19	b.	b.	PROPN
ejpam-3422	43	20	we	we	PRON
ejpam-3422	43	21	call	call	VERB
ejpam-3422	43	22	“	"	PUNCT
ejpam-3422	43	23	�	�	PROPN
ejpam-3422	43	24	”	"	PUNCT
ejpam-3422	43	25	a	a	DET
ejpam-3422	43	26	hyperorder	hyperorder	NOUN
ejpam-3422	43	27	on	on	ADP
ejpam-3422	43	28	h.	h.	PROPN
ejpam-3422	43	29	definition	definition	NOUN
ejpam-3422	43	30	2.1	2.1	NUM
ejpam-3422	43	31	.	.	PUNCT
ejpam-3422	44	1	[	[	X
ejpam-3422	44	2	4	4	X
ejpam-3422	44	3	]	]	PUNCT
ejpam-3422	44	4	let	let	VERB
ejpam-3422	44	5	h	h	NOUN
ejpam-3422	44	6	be	be	AUX
ejpam-3422	44	7	a	a	DET
ejpam-3422	44	8	nonempty	nonempty	ADV
ejpam-3422	44	9	set	set	VERB
ejpam-3422	44	10	and	and	CCONJ
ejpam-3422	44	11	~	~	PUNCT
ejpam-3422	44	12	be	be	AUX
ejpam-3422	44	13	a	a	DET
ejpam-3422	44	14	hyperoperation	hyperoperation	NOUN
ejpam-3422	44	15	on	on	ADP
ejpam-3422	44	16	h.	h.	PROPN
ejpam-3422	44	17	then	then	ADV
ejpam-3422	44	18	(	(	PUNCT
ejpam-3422	44	19	h;~	h;~	NOUN
ejpam-3422	44	20	,	,	PUNCT
ejpam-3422	44	21	0	0	NUM
ejpam-3422	44	22	)	)	PUNCT
ejpam-3422	44	23	is	be	AUX
ejpam-3422	44	24	called	call	VERB
ejpam-3422	44	25	a	a	DET
ejpam-3422	44	26	hyper	hyper	ADJ
ejpam-3422	44	27	gr	gr	NOUN
ejpam-3422	44	28	-	-	PUNCT
ejpam-3422	44	29	algebra	algebra	NOUN
ejpam-3422	44	30	if	if	SCONJ
ejpam-3422	44	31	it	it	PRON
ejpam-3422	44	32	contains	contain	VERB
ejpam-3422	44	33	a	a	DET
ejpam-3422	44	34	constant	constant	ADJ
ejpam-3422	44	35	0	0	NUM
ejpam-3422	44	36	∈	∈	NOUN
ejpam-3422	44	37	h	h	NOUN
ejpam-3422	44	38	and	and	CCONJ
ejpam-3422	44	39	it	it	PRON
ejpam-3422	44	40	satisfies	satisfy	VERB
ejpam-3422	44	41	the	the	DET
ejpam-3422	44	42	following	follow	VERB
ejpam-3422	44	43	conditions	condition	NOUN
ejpam-3422	44	44	,	,	PUNCT
ejpam-3422	44	45	for	for	ADP
ejpam-3422	44	46	all	all	DET
ejpam-3422	44	47	x	x	NOUN
ejpam-3422	44	48	,	,	PUNCT
ejpam-3422	44	49	y	y	PROPN
ejpam-3422	44	50	,	,	PUNCT
ejpam-3422	44	51	z	z	PROPN
ejpam-3422	44	52	∈	∈	PROPN
ejpam-3422	44	53	h	h	NOUN
ejpam-3422	44	54	:	:	PUNCT
ejpam-3422	44	55	(	(	PUNCT
ejpam-3422	44	56	hgr1	hgr1	PROPN
ejpam-3422	44	57	)	)	PUNCT
ejpam-3422	45	1	(	(	PUNCT
ejpam-3422	45	2	x~	x~	PROPN
ejpam-3422	45	3	z	z	PROPN
ejpam-3422	45	4	)	)	PUNCT
ejpam-3422	45	5	~	~	PUNCT
ejpam-3422	45	6	(	(	PUNCT
ejpam-3422	45	7	y	y	X
ejpam-3422	45	8	~	~	PUNCT
ejpam-3422	45	9	z	z	X
ejpam-3422	45	10	)	)	PUNCT
ejpam-3422	45	11	�	�	PROPN
ejpam-3422	45	12	x~	x~	NUM
ejpam-3422	45	13	y	y	PROPN
ejpam-3422	45	14	;	;	PUNCT
ejpam-3422	45	15	(	(	PUNCT
ejpam-3422	45	16	hgr2	hgr2	NOUN
ejpam-3422	45	17	)	)	PUNCT
ejpam-3422	45	18	(	(	PUNCT
ejpam-3422	46	1	x~	x~	PROPN
ejpam-3422	46	2	y	y	NUM
ejpam-3422	46	3	)	)	PUNCT
ejpam-3422	46	4	~	~	PUNCT
ejpam-3422	46	5	z	z	X
ejpam-3422	46	6	=	=	SYM
ejpam-3422	46	7	(	(	PUNCT
ejpam-3422	46	8	x~	x~	PROPN
ejpam-3422	46	9	z	z	PROPN
ejpam-3422	46	10	)	)	PUNCT
ejpam-3422	46	11	~	~	PUNCT
ejpam-3422	46	12	y	y	X
ejpam-3422	46	13	;	;	PUNCT
ejpam-3422	46	14	(	(	PUNCT
ejpam-3422	46	15	hgr3	hgr3	PROPN
ejpam-3422	46	16	)	)	PUNCT
ejpam-3422	46	17	x	x	NOUN
ejpam-3422	46	18	�	�	PROPN
ejpam-3422	46	19	x	x	SYM
ejpam-3422	46	20	;	;	PUNCT
ejpam-3422	46	21	(	(	PUNCT
ejpam-3422	46	22	hgr4	hgr4	NOUN
ejpam-3422	46	23	)	)	PUNCT
ejpam-3422	46	24	0	0	NUM
ejpam-3422	46	25	~	~	PUNCT
ejpam-3422	46	26	(	(	PUNCT
ejpam-3422	46	27	0	0	NUM
ejpam-3422	46	28	~	~	SYM
ejpam-3422	46	29	x	x	X
ejpam-3422	46	30	)	)	PUNCT
ejpam-3422	46	31	�	�	PROPN
ejpam-3422	46	32	x	x	SYM
ejpam-3422	46	33	,	,	PUNCT
ejpam-3422	46	34	x	x	PROPN
ejpam-3422	46	35	6=	6=	ADP
ejpam-3422	46	36	0	0	NUM
ejpam-3422	46	37	;	;	PUNCT
ejpam-3422	46	38	and	and	CCONJ
ejpam-3422	46	39	(	(	PUNCT
ejpam-3422	46	40	hgr5	hgr5	PROPN
ejpam-3422	46	41	)	)	PUNCT
ejpam-3422	46	42	(	(	PUNCT
ejpam-3422	46	43	x~	x~	PROPN
ejpam-3422	46	44	y	y	NUM
ejpam-3422	46	45	)	)	PUNCT
ejpam-3422	46	46	~	~	PUNCT
ejpam-3422	46	47	z	z	X
ejpam-3422	46	48	�	�	PROPN
ejpam-3422	46	49	y	y	PROPN
ejpam-3422	46	50	~	~	PUNCT
ejpam-3422	46	51	z.	z.	PROPN
ejpam-3422	46	52	for	for	ADP
ejpam-3422	46	53	the	the	DET
ejpam-3422	46	54	sake	sake	NOUN
ejpam-3422	46	55	of	of	ADP
ejpam-3422	46	56	simplicity	simplicity	NOUN
ejpam-3422	46	57	,	,	PUNCT
ejpam-3422	46	58	we	we	PRON
ejpam-3422	46	59	also	also	ADV
ejpam-3422	46	60	call	call	VERB
ejpam-3422	46	61	h	h	NOUN
ejpam-3422	46	62	a	a	DET
ejpam-3422	46	63	hyper	hyper	ADJ
ejpam-3422	46	64	gr	gr	NOUN
ejpam-3422	46	65	-	-	PUNCT
ejpam-3422	46	66	algebra	algebra	NOUN
ejpam-3422	46	67	.	.	PUNCT
ejpam-3422	47	1	example	example	NOUN
ejpam-3422	47	2	2.2	2.2	NUM
ejpam-3422	47	3	.	.	PUNCT
ejpam-3422	48	1	consider	consider	VERB
ejpam-3422	48	2	a	a	DET
ejpam-3422	48	3	set	set	NOUN
ejpam-3422	48	4	h	h	NOUN
ejpam-3422	48	5	=	=	SYM
ejpam-3422	48	6	{	{	PUNCT
ejpam-3422	48	7	0	0	NUM
ejpam-3422	48	8	,	,	PUNCT
ejpam-3422	48	9	1	1	NUM
ejpam-3422	48	10	,	,	PUNCT
ejpam-3422	48	11	2	2	NUM
ejpam-3422	48	12	,	,	PUNCT
ejpam-3422	48	13	3	3	NUM
ejpam-3422	48	14	}	}	PUNCT
ejpam-3422	48	15	with	with	ADP
ejpam-3422	48	16	the	the	DET
ejpam-3422	48	17	cayley	cayley	ADJ
ejpam-3422	48	18	table	table	NOUN
ejpam-3422	48	19	below	below	ADV
ejpam-3422	48	20	.	.	PUNCT
ejpam-3422	49	1	~	~	PUNCT
ejpam-3422	49	2	0	0	NUM
ejpam-3422	50	1	1	1	NUM
ejpam-3422	50	2	2	2	NUM
ejpam-3422	50	3	3	3	NUM
ejpam-3422	50	4	0	0	NUM
ejpam-3422	50	5	{	{	PUNCT
ejpam-3422	50	6	0	0	NUM
ejpam-3422	50	7	,	,	PUNCT
ejpam-3422	50	8	1	1	NUM
ejpam-3422	50	9	}	}	PUNCT
ejpam-3422	50	10	{	{	PUNCT
ejpam-3422	50	11	0	0	NUM
ejpam-3422	50	12	,	,	PUNCT
ejpam-3422	50	13	1	1	NUM
ejpam-3422	50	14	}	}	PUNCT
ejpam-3422	50	15	{	{	PUNCT
ejpam-3422	50	16	0	0	NUM
ejpam-3422	50	17	,	,	PUNCT
ejpam-3422	50	18	1	1	NUM
ejpam-3422	50	19	}	}	PUNCT
ejpam-3422	50	20	{	{	PUNCT
ejpam-3422	50	21	0	0	NUM
ejpam-3422	50	22	,	,	PUNCT
ejpam-3422	50	23	1	1	NUM
ejpam-3422	50	24	}	}	SYM
ejpam-3422	50	25	1	1	NUM
ejpam-3422	50	26	{	{	PUNCT
ejpam-3422	50	27	1	1	NUM
ejpam-3422	50	28	}	}	PUNCT
ejpam-3422	50	29	{	{	PUNCT
ejpam-3422	50	30	0	0	NUM
ejpam-3422	50	31	,	,	PUNCT
ejpam-3422	50	32	1	1	NUM
ejpam-3422	50	33	}	}	PUNCT
ejpam-3422	50	34	{	{	PUNCT
ejpam-3422	50	35	0	0	NUM
ejpam-3422	50	36	,	,	PUNCT
ejpam-3422	50	37	1	1	NUM
ejpam-3422	50	38	}	}	PUNCT
ejpam-3422	50	39	{	{	PUNCT
ejpam-3422	50	40	0	0	NUM
ejpam-3422	50	41	,	,	PUNCT
ejpam-3422	50	42	1	1	NUM
ejpam-3422	50	43	}	}	SYM
ejpam-3422	50	44	2	2	NUM
ejpam-3422	50	45	{	{	PUNCT
ejpam-3422	50	46	0	0	NUM
ejpam-3422	50	47	,	,	PUNCT
ejpam-3422	50	48	2	2	NUM
ejpam-3422	50	49	}	}	PUNCT
ejpam-3422	50	50	{	{	PUNCT
ejpam-3422	50	51	0	0	NUM
ejpam-3422	50	52	,	,	PUNCT
ejpam-3422	50	53	2	2	NUM
ejpam-3422	50	54	}	}	PUNCT
ejpam-3422	50	55	{	{	PUNCT
ejpam-3422	50	56	0	0	NUM
ejpam-3422	50	57	,	,	PUNCT
ejpam-3422	50	58	1	1	NUM
ejpam-3422	50	59	,	,	PUNCT
ejpam-3422	50	60	2	2	NUM
ejpam-3422	50	61	}	}	PUNCT
ejpam-3422	50	62	{	{	PUNCT
ejpam-3422	50	63	0	0	NUM
ejpam-3422	50	64	,	,	PUNCT
ejpam-3422	50	65	1	1	NUM
ejpam-3422	50	66	,	,	PUNCT
ejpam-3422	50	67	2	2	NUM
ejpam-3422	50	68	}	}	SYM
ejpam-3422	50	69	3	3	NUM
ejpam-3422	50	70	{	{	PUNCT
ejpam-3422	50	71	0	0	NUM
ejpam-3422	50	72	,	,	PUNCT
ejpam-3422	50	73	3	3	NUM
ejpam-3422	50	74	}	}	PUNCT
ejpam-3422	50	75	{	{	PUNCT
ejpam-3422	50	76	0	0	NUM
ejpam-3422	50	77	,	,	PUNCT
ejpam-3422	50	78	3	3	NUM
ejpam-3422	50	79	}	}	PUNCT
ejpam-3422	50	80	{	{	PUNCT
ejpam-3422	50	81	0	0	NUM
ejpam-3422	50	82	,	,	PUNCT
ejpam-3422	50	83	3	3	NUM
ejpam-3422	50	84	}	}	PUNCT
ejpam-3422	50	85	{	{	PUNCT
ejpam-3422	50	86	0	0	NUM
ejpam-3422	50	87	,	,	PUNCT
ejpam-3422	50	88	1	1	NUM
ejpam-3422	50	89	,	,	PUNCT
ejpam-3422	50	90	3	3	NUM
ejpam-3422	50	91	}	}	PUNCT
ejpam-3422	50	92	a.	a.	NOUN
ejpam-3422	50	93	macodi	macodi	NOUN
ejpam-3422	50	94	-	-	PUNCT
ejpam-3422	50	95	ringia	ringia	ADJ
ejpam-3422	50	96	,	,	PUNCT
ejpam-3422	50	97	g.	g.	PROPN
ejpam-3422	50	98	petalcorin	petalcorin	PROPN
ejpam-3422	50	99	,	,	PUNCT
ejpam-3422	50	100	jr	jr	PROPN
ejpam-3422	50	101	.	.	PROPN
ejpam-3422	50	102	/	/	SYM
ejpam-3422	50	103	eur	eur	PROPN
ejpam-3422	50	104	.	.	PUNCT
ejpam-3422	51	1	j.	j.	PROPN
ejpam-3422	51	2	pure	pure	PROPN
ejpam-3422	51	3	appl	appl	PROPN
ejpam-3422	51	4	.	.	PROPN
ejpam-3422	51	5	math	math	PROPN
ejpam-3422	51	6	,	,	PUNCT
ejpam-3422	51	7	12	12	NUM
ejpam-3422	51	8	(	(	PUNCT
ejpam-3422	51	9	2	2	NUM
ejpam-3422	51	10	)	)	PUNCT
ejpam-3422	51	11	(	(	PUNCT
ejpam-3422	51	12	2019	2019	NUM
ejpam-3422	51	13	)	)	PUNCT
ejpam-3422	51	14	,	,	PUNCT
ejpam-3422	51	15	409	409	NUM
ejpam-3422	51	16	-	-	SYM
ejpam-3422	51	17	417	417	NUM
ejpam-3422	51	18	411	411	NUM
ejpam-3422	51	19	it	it	PRON
ejpam-3422	51	20	can	can	AUX
ejpam-3422	51	21	be	be	AUX
ejpam-3422	51	22	verified	verify	VERB
ejpam-3422	51	23	that	that	SCONJ
ejpam-3422	51	24	h	h	NOUN
ejpam-3422	51	25	is	be	AUX
ejpam-3422	51	26	a	a	DET
ejpam-3422	51	27	hyper	hyper	ADJ
ejpam-3422	51	28	gr	gr	NOUN
ejpam-3422	51	29	-	-	NOUN
ejpam-3422	51	30	algebra	algebra	NOUN
ejpam-3422	51	31	.	.	PUNCT
ejpam-3422	52	1	definition	definition	NOUN
ejpam-3422	52	2	2.3	2.3	NUM
ejpam-3422	52	3	.	.	PUNCT
ejpam-3422	53	1	[	[	X
ejpam-3422	53	2	4	4	X
ejpam-3422	53	3	]	]	PUNCT
ejpam-3422	53	4	let	let	VERB
ejpam-3422	53	5	h	h	PRON
ejpam-3422	53	6	be	be	AUX
ejpam-3422	53	7	a	a	DET
ejpam-3422	53	8	hyper	hyper	ADJ
ejpam-3422	53	9	gr	gr	NOUN
ejpam-3422	53	10	-	-	PUNCT
ejpam-3422	53	11	algebra	algebra	NOUN
ejpam-3422	53	12	and	and	CCONJ
ejpam-3422	53	13	s	s	AUX
ejpam-3422	53	14	be	be	AUX
ejpam-3422	53	15	a	a	DET
ejpam-3422	53	16	subset	subset	NOUN
ejpam-3422	53	17	of	of	ADP
ejpam-3422	53	18	h	h	NOUN
ejpam-3422	53	19	containing	contain	VERB
ejpam-3422	53	20	0	0	NUM
ejpam-3422	53	21	.	.	PUNCT
ejpam-3422	54	1	if	if	SCONJ
ejpam-3422	54	2	s	s	PROPN
ejpam-3422	54	3	is	be	AUX
ejpam-3422	54	4	a	a	DET
ejpam-3422	54	5	hyper	hyper	ADJ
ejpam-3422	54	6	gr	gr	NOUN
ejpam-3422	54	7	-	-	NOUN
ejpam-3422	54	8	algebra	algebra	NOUN
ejpam-3422	54	9	with	with	ADP
ejpam-3422	54	10	respect	respect	NOUN
ejpam-3422	54	11	to	to	ADP
ejpam-3422	54	12	the	the	DET
ejpam-3422	54	13	hyperoperation	hyperoperation	NOUN
ejpam-3422	54	14	~	~	PUNCT
ejpam-3422	54	15	on	on	ADP
ejpam-3422	54	16	h	h	NOUN
ejpam-3422	54	17	,	,	PUNCT
ejpam-3422	54	18	then	then	ADV
ejpam-3422	54	19	we	we	PRON
ejpam-3422	54	20	say	say	VERB
ejpam-3422	54	21	that	that	PRON
ejpam-3422	54	22	s	s	VERB
ejpam-3422	54	23	is	be	AUX
ejpam-3422	54	24	a	a	DET
ejpam-3422	54	25	hyper	hyper	ADJ
ejpam-3422	54	26	subgr	subgr	NOUN
ejpam-3422	54	27	-	-	PUNCT
ejpam-3422	54	28	algebra	algebra	NOUN
ejpam-3422	54	29	on	on	ADP
ejpam-3422	54	30	h.	h.	PROPN
ejpam-3422	54	31	theorem	theorem	PROPN
ejpam-3422	54	32	2.4	2.4	NUM
ejpam-3422	54	33	.	.	PUNCT
ejpam-3422	55	1	[	[	X
ejpam-3422	55	2	4](hyper	4](hyper	NUM
ejpam-3422	55	3	subgr	subgr	ADJ
ejpam-3422	55	4	-	-	PUNCT
ejpam-3422	55	5	algebra	algebra	NOUN
ejpam-3422	55	6	criterion	criterion	NOUN
ejpam-3422	55	7	)	)	PUNCT
ejpam-3422	55	8	let	let	VERB
ejpam-3422	55	9	h	h	NOUN
ejpam-3422	55	10	be	be	AUX
ejpam-3422	55	11	a	a	DET
ejpam-3422	55	12	hyper	hyper	ADJ
ejpam-3422	55	13	gr	gr	NOUN
ejpam-3422	55	14	-	-	PUNCT
ejpam-3422	55	15	algebra	algebra	NOUN
ejpam-3422	55	16	and	and	CCONJ
ejpam-3422	55	17	s	s	AUX
ejpam-3422	55	18	be	be	AUX
ejpam-3422	55	19	a	a	DET
ejpam-3422	55	20	non	non	ADJ
ejpam-3422	55	21	-	-	ADJ
ejpam-3422	55	22	empty	empty	ADJ
ejpam-3422	55	23	subset	subset	NOUN
ejpam-3422	55	24	of	of	ADP
ejpam-3422	55	25	h.	h.	PROPN
ejpam-3422	56	1	then	then	ADV
ejpam-3422	56	2	s	s	VERB
ejpam-3422	56	3	is	be	AUX
ejpam-3422	56	4	a	a	DET
ejpam-3422	56	5	hyper	hyper	ADJ
ejpam-3422	56	6	subgr	subgr	NOUN
ejpam-3422	56	7	-	-	PUNCT
ejpam-3422	56	8	algebra	algebra	NOUN
ejpam-3422	56	9	of	of	ADP
ejpam-3422	56	10	h	h	NOUN
ejpam-3422	56	11	if	if	SCONJ
ejpam-3422	56	12	and	and	CCONJ
ejpam-3422	56	13	only	only	ADV
ejpam-3422	56	14	if	if	SCONJ
ejpam-3422	56	15	(	(	PUNCT
ejpam-3422	56	16	x~	x~	PROPN
ejpam-3422	56	17	y	y	X
ejpam-3422	56	18	)	)	PUNCT
ejpam-3422	56	19	⊆	⊆	NUM
ejpam-3422	56	20	s	s	NOUN
ejpam-3422	56	21	for	for	ADP
ejpam-3422	56	22	all	all	DET
ejpam-3422	56	23	x	x	NOUN
ejpam-3422	56	24	,	,	PUNCT
ejpam-3422	56	25	y	y	PROPN
ejpam-3422	56	26	∈	∈	PROPN
ejpam-3422	56	27	s.	s.	PROPN
ejpam-3422	56	28	definition	definition	NOUN
ejpam-3422	56	29	2.5	2.5	NUM
ejpam-3422	56	30	.	.	PUNCT
ejpam-3422	57	1	[	[	X
ejpam-3422	57	2	4	4	X
ejpam-3422	57	3	]	]	PUNCT
ejpam-3422	57	4	let	let	VERB
ejpam-3422	57	5	i	i	PRON
ejpam-3422	57	6	be	be	AUX
ejpam-3422	57	7	a	a	DET
ejpam-3422	57	8	subset	subset	NOUN
ejpam-3422	57	9	of	of	ADP
ejpam-3422	57	10	a	a	DET
ejpam-3422	57	11	hyper	hyper	ADJ
ejpam-3422	57	12	gr	gr	NOUN
ejpam-3422	57	13	-	-	PUNCT
ejpam-3422	57	14	algebra	algebra	NOUN
ejpam-3422	57	15	h.	h.	NOUN
ejpam-3422	57	16	then	then	ADV
ejpam-3422	57	17	i	i	PRON
ejpam-3422	57	18	is	be	AUX
ejpam-3422	57	19	said	say	VERB
ejpam-3422	57	20	to	to	PART
ejpam-3422	57	21	be	be	AUX
ejpam-3422	57	22	a	a	DET
ejpam-3422	57	23	hyper	hyper	ADJ
ejpam-3422	57	24	gr	gr	NOUN
ejpam-3422	57	25	-	-	PUNCT
ejpam-3422	57	26	ideal	ideal	NOUN
ejpam-3422	57	27	of	of	ADP
ejpam-3422	57	28	h	h	NOUN
ejpam-3422	57	29	if	if	SCONJ
ejpam-3422	57	30	i	i	PRON
ejpam-3422	57	31	)	)	PUNCT
ejpam-3422	57	32	0	0	PUNCT
ejpam-3422	58	1	∈	∈	PROPN
ejpam-3422	58	2	i	i	PRON
ejpam-3422	58	3	;	;	PUNCT
ejpam-3422	58	4	and	and	CCONJ
ejpam-3422	58	5	ii	ii	X
ejpam-3422	58	6	)	)	PUNCT
ejpam-3422	58	7	for	for	ADP
ejpam-3422	58	8	all	all	DET
ejpam-3422	58	9	x	x	NOUN
ejpam-3422	58	10	,	,	PUNCT
ejpam-3422	58	11	y	y	PROPN
ejpam-3422	58	12	∈	∈	PROPN
ejpam-3422	58	13	h	h	NOUN
ejpam-3422	58	14	,	,	PUNCT
ejpam-3422	58	15	x~	x~	PROPN
ejpam-3422	58	16	y	y	PROPN
ejpam-3422	58	17	⊆	⊆	NUM
ejpam-3422	58	18	i	i	PROPN
ejpam-3422	58	19	and	and	CCONJ
ejpam-3422	58	20	y	y	PROPN
ejpam-3422	58	21	∈	∈	PROPN
ejpam-3422	59	1	i	i	PRON
ejpam-3422	59	2	imply	imply	VERB
ejpam-3422	59	3	that	that	SCONJ
ejpam-3422	59	4	x	x	X
ejpam-3422	59	5	∈	∈	PROPN
ejpam-3422	59	6	i.	i.	NOUN
ejpam-3422	59	7	definition	definition	NOUN
ejpam-3422	59	8	2.6	2.6	NUM
ejpam-3422	59	9	.	.	PUNCT
ejpam-3422	60	1	[	[	X
ejpam-3422	60	2	8	8	NUM
ejpam-3422	60	3	]	]	PUNCT
ejpam-3422	60	4	by	by	ADP
ejpam-3422	60	5	a	a	DET
ejpam-3422	60	6	hyper	hyper	ADJ
ejpam-3422	60	7	bck	bck	NOUN
ejpam-3422	60	8	-	-	PUNCT
ejpam-3422	60	9	algebra	algebra	NOUN
ejpam-3422	60	10	we	we	PRON
ejpam-3422	60	11	mean	mean	VERB
ejpam-3422	61	1	a	a	DET
ejpam-3422	61	2	non	non	ADJ
ejpam-3422	61	3	-	-	ADJ
ejpam-3422	61	4	empty	empty	ADJ
ejpam-3422	61	5	set	set	ADJ
ejpam-3422	61	6	h	h	NOUN
ejpam-3422	61	7	endowed	endow	VERB
ejpam-3422	61	8	with	with	ADP
ejpam-3422	61	9	a	a	DET
ejpam-3422	61	10	hyperoperation	hyperoperation	NOUN
ejpam-3422	61	11	“	"	PUNCT
ejpam-3422	61	12	◦	◦	NOUN
ejpam-3422	61	13	′′	′′	PROPN
ejpam-3422	61	14	and	and	CCONJ
ejpam-3422	61	15	a	a	DET
ejpam-3422	61	16	constant	constant	ADJ
ejpam-3422	61	17	0	0	NUM
ejpam-3422	61	18	satisfying	satisfy	VERB
ejpam-3422	61	19	the	the	DET
ejpam-3422	61	20	following	follow	VERB
ejpam-3422	61	21	axioms	axiom	NOUN
ejpam-3422	61	22	:	:	PUNCT
ejpam-3422	61	23	(	(	PUNCT
ejpam-3422	61	24	hk1	hk1	NOUN
ejpam-3422	61	25	)	)	PUNCT
ejpam-3422	61	26	(	(	PUNCT
ejpam-3422	61	27	x	x	X
ejpam-3422	61	28	◦	◦	NOUN
ejpam-3422	61	29	z	z	NOUN
ejpam-3422	61	30	)	)	PUNCT
ejpam-3422	61	31	~	~	PUNCT
ejpam-3422	61	32	(	(	PUNCT
ejpam-3422	61	33	y	y	PROPN
ejpam-3422	61	34	◦	◦	PROPN
ejpam-3422	61	35	z	z	PROPN
ejpam-3422	61	36	)	)	PUNCT
ejpam-3422	61	37	�	�	PROPN
ejpam-3422	61	38	x	x	PUNCT
ejpam-3422	61	39	◦	◦	NOUN
ejpam-3422	61	40	y	y	PROPN
ejpam-3422	61	41	,	,	PUNCT
ejpam-3422	61	42	(	(	PUNCT
ejpam-3422	61	43	hk2	hk2	X
ejpam-3422	61	44	)	)	PUNCT
ejpam-3422	61	45	(	(	PUNCT
ejpam-3422	61	46	x	x	X
ejpam-3422	61	47	◦	◦	VERB
ejpam-3422	61	48	y	y	NOUN
ejpam-3422	61	49	)	)	PUNCT
ejpam-3422	61	50	◦	◦	NOUN
ejpam-3422	61	51	z	z	NOUN
ejpam-3422	61	52	=	=	SYM
ejpam-3422	61	53	(	(	PUNCT
ejpam-3422	61	54	x	x	PART
ejpam-3422	61	55	◦	◦	NOUN
ejpam-3422	61	56	z	z	NOUN
ejpam-3422	61	57	)	)	PUNCT
ejpam-3422	61	58	◦	◦	NOUN
ejpam-3422	61	59	y	y	PROPN
ejpam-3422	61	60	,	,	PUNCT
ejpam-3422	61	61	(	(	PUNCT
ejpam-3422	61	62	hk3	hk3	NOUN
ejpam-3422	61	63	)	)	PUNCT
ejpam-3422	61	64	x	x	SYM
ejpam-3422	61	65	◦	◦	NOUN
ejpam-3422	61	66	h	h	NOUN
ejpam-3422	61	67	�	�	NOUN
ejpam-3422	61	68	{	{	PUNCT
ejpam-3422	61	69	x	x	NOUN
ejpam-3422	61	70	}	}	PUNCT
ejpam-3422	61	71	,	,	PUNCT
ejpam-3422	61	72	(	(	PUNCT
ejpam-3422	61	73	hk4	hk4	X
ejpam-3422	61	74	)	)	PUNCT
ejpam-3422	61	75	x	x	NOUN
ejpam-3422	61	76	�	�	PROPN
ejpam-3422	61	77	y	y	PROPN
ejpam-3422	61	78	and	and	CCONJ
ejpam-3422	61	79	y	y	PROPN
ejpam-3422	61	80	�	�	PROPN
ejpam-3422	61	81	x	x	PUNCT
ejpam-3422	61	82	imply	imply	VERB
ejpam-3422	61	83	x	x	X
ejpam-3422	61	84	=	=	SYM
ejpam-3422	61	85	y	y	PROPN
ejpam-3422	61	86	,	,	PUNCT
ejpam-3422	61	87	for	for	ADP
ejpam-3422	61	88	all	all	DET
ejpam-3422	61	89	x	x	NOUN
ejpam-3422	61	90	,	,	PUNCT
ejpam-3422	61	91	y	y	PROPN
ejpam-3422	61	92	,	,	PUNCT
ejpam-3422	61	93	z	z	NOUN
ejpam-3422	61	94	∈	∈	PROPN
ejpam-3422	61	95	h	h	NOUN
ejpam-3422	61	96	where	where	SCONJ
ejpam-3422	61	97	x	x	X
ejpam-3422	61	98	�	�	PROPN
ejpam-3422	61	99	y	y	PROPN
ejpam-3422	61	100	is	be	AUX
ejpam-3422	61	101	defined	define	VERB
ejpam-3422	61	102	by	by	ADP
ejpam-3422	61	103	0	0	NUM
ejpam-3422	61	104	∈	∈	PROPN
ejpam-3422	61	105	x	x	PUNCT
ejpam-3422	61	106	◦	◦	NOUN
ejpam-3422	61	107	y	y	PROPN
ejpam-3422	61	108	and	and	CCONJ
ejpam-3422	61	109	for	for	ADP
ejpam-3422	61	110	every	every	DET
ejpam-3422	61	111	a	a	PROPN
ejpam-3422	61	112	,	,	PUNCT
ejpam-3422	61	113	b	b	PROPN
ejpam-3422	61	114	⊆	⊆	NUM
ejpam-3422	61	115	h	h	NOUN
ejpam-3422	61	116	,	,	PUNCT
ejpam-3422	61	117	a	a	DET
ejpam-3422	61	118	�	�	PROPN
ejpam-3422	61	119	b	b	PROPN
ejpam-3422	61	120	is	be	AUX
ejpam-3422	61	121	defined	define	VERB
ejpam-3422	61	122	by	by	ADP
ejpam-3422	61	123	for	for	ADP
ejpam-3422	61	124	all	all	DET
ejpam-3422	61	125	a	a	DET
ejpam-3422	61	126	∈	∈	PROPN
ejpam-3422	61	127	a	a	PRON
ejpam-3422	61	128	,	,	PUNCT
ejpam-3422	61	129	there	there	PRON
ejpam-3422	61	130	exist	exist	VERB
ejpam-3422	61	131	b	b	PROPN
ejpam-3422	61	132	∈	∈	PROPN
ejpam-3422	61	133	b	b	NOUN
ejpam-3422	61	134	such	such	ADJ
ejpam-3422	61	135	that	that	SCONJ
ejpam-3422	61	136	a	a	DET
ejpam-3422	61	137	�	�	PROPN
ejpam-3422	61	138	b.	b.	PROPN
ejpam-3422	61	139	definition	definition	NOUN
ejpam-3422	61	140	2.7	2.7	NUM
ejpam-3422	61	141	.	.	PUNCT
ejpam-3422	62	1	[	[	X
ejpam-3422	62	2	1	1	X
ejpam-3422	62	3	]	]	PUNCT
ejpam-3422	62	4	let	let	VERB
ejpam-3422	62	5	i	i	PRON
ejpam-3422	62	6	be	be	AUX
ejpam-3422	62	7	a	a	DET
ejpam-3422	62	8	non	non	ADJ
ejpam-3422	62	9	-	-	ADJ
ejpam-3422	62	10	empty	empty	ADJ
ejpam-3422	62	11	subset	subset	NOUN
ejpam-3422	62	12	of	of	ADP
ejpam-3422	62	13	h	h	NOUN
ejpam-3422	62	14	and	and	CCONJ
ejpam-3422	62	15	0	0	NUM
ejpam-3422	62	16	∈	∈	PROPN
ejpam-3422	62	17	h.	h.	NOUN
ejpam-3422	63	1	then	then	ADV
ejpam-3422	63	2	i	i	PRON
ejpam-3422	63	3	is	be	AUX
ejpam-3422	63	4	called	call	VERB
ejpam-3422	63	5	a	a	DET
ejpam-3422	63	6	weak	weak	ADJ
ejpam-3422	63	7	implicative	implicative	ADJ
ejpam-3422	63	8	hyper	hyper	ADJ
ejpam-3422	63	9	bck	bck	NOUN
ejpam-3422	63	10	-	-	PUNCT
ejpam-3422	63	11	ideal	ideal	NOUN
ejpam-3422	63	12	of	of	ADP
ejpam-3422	63	13	h	h	NOUN
ejpam-3422	63	14	if	if	SCONJ
ejpam-3422	63	15	,	,	PUNCT
ejpam-3422	63	16	(	(	PUNCT
ejpam-3422	63	17	x	x	X
ejpam-3422	63	18	◦	◦	NOUN
ejpam-3422	63	19	z	z	NOUN
ejpam-3422	63	20	)	)	PUNCT
ejpam-3422	63	21	◦	◦	NOUN
ejpam-3422	63	22	(	(	PUNCT
ejpam-3422	63	23	y	y	PROPN
ejpam-3422	63	24	◦	◦	NOUN
ejpam-3422	63	25	x	x	X
ejpam-3422	63	26	)	)	PUNCT
ejpam-3422	64	1	⊂	⊂	PROPN
ejpam-3422	65	1	i	i	PRON
ejpam-3422	65	2	and	and	CCONJ
ejpam-3422	65	3	z	z	NOUN
ejpam-3422	65	4	∈	∈	PROPN
ejpam-3422	66	1	i	i	PRON
ejpam-3422	66	2	imply	imply	VERB
ejpam-3422	66	3	x	x	X
ejpam-3422	66	4	∈	∈	PROPN
ejpam-3422	66	5	i	i	PRON
ejpam-3422	66	6	,	,	PUNCT
ejpam-3422	66	7	for	for	ADP
ejpam-3422	66	8	all	all	DET
ejpam-3422	66	9	x	x	NOUN
ejpam-3422	66	10	,	,	PUNCT
ejpam-3422	66	11	y	y	PROPN
ejpam-3422	66	12	,	,	PUNCT
ejpam-3422	66	13	z	z	PROPN
ejpam-3422	66	14	∈	∈	PROPN
ejpam-3422	66	15	h.	h.	NOUN
ejpam-3422	66	16	definition	definition	NOUN
ejpam-3422	66	17	2.8	2.8	NUM
ejpam-3422	66	18	.	.	PUNCT
ejpam-3422	67	1	[	[	X
ejpam-3422	67	2	17	17	NUM
ejpam-3422	67	3	]	]	PUNCT
ejpam-3422	67	4	let	let	VERB
ejpam-3422	67	5	m	m	PRON
ejpam-3422	67	6	be	be	AUX
ejpam-3422	67	7	a	a	DET
ejpam-3422	67	8	nonempty	nonempty	ADV
ejpam-3422	67	9	set	set	VERB
ejpam-3422	67	10	.	.	PUNCT
ejpam-3422	68	1	a	a	DET
ejpam-3422	68	2	fuzzy	fuzzy	ADJ
ejpam-3422	68	3	set	set	VERB
ejpam-3422	68	4	µ	µ	NOUN
ejpam-3422	68	5	in	in	ADP
ejpam-3422	68	6	m	m	PROPN
ejpam-3422	68	7	is	be	AUX
ejpam-3422	68	8	a	a	DET
ejpam-3422	68	9	function	function	NOUN
ejpam-3422	68	10	µ	µ	NOUN
ejpam-3422	68	11	:	:	PUNCT
ejpam-3422	68	12	m	m	VERB
ejpam-3422	68	13	→	→	SYM
ejpam-3422	69	1	[	[	X
ejpam-3422	69	2	0	0	NUM
ejpam-3422	69	3	,	,	PUNCT
ejpam-3422	69	4	1	1	NUM
ejpam-3422	69	5	]	]	PUNCT
ejpam-3422	69	6	.	.	PUNCT
ejpam-3422	70	1	definition	definition	NOUN
ejpam-3422	70	2	2.9	2.9	NUM
ejpam-3422	70	3	.	.	PUNCT
ejpam-3422	71	1	[	[	X
ejpam-3422	71	2	3	3	X
ejpam-3422	71	3	]	]	X
ejpam-3422	71	4	let	let	VERB
ejpam-3422	71	5	µ	µ	X
ejpam-3422	71	6	be	be	AUX
ejpam-3422	71	7	a	a	DET
ejpam-3422	71	8	fuzzy	fuzzy	ADJ
ejpam-3422	71	9	set	set	NOUN
ejpam-3422	71	10	in	in	ADP
ejpam-3422	71	11	m	m	PROPN
ejpam-3422	71	12	.	.	PUNCT
ejpam-3422	72	1	for	for	ADP
ejpam-3422	72	2	a	a	DET
ejpam-3422	72	3	fixed	fix	VERB
ejpam-3422	72	4	t	t	NOUN
ejpam-3422	72	5	∈	∈	PROPN
ejpam-3422	73	1	[	[	X
ejpam-3422	73	2	0	0	NUM
ejpam-3422	73	3	,	,	PUNCT
ejpam-3422	73	4	1	1	NUM
ejpam-3422	73	5	]	]	PUNCT
ejpam-3422	73	6	,	,	PUNCT
ejpam-3422	73	7	the	the	DET
ejpam-3422	73	8	set	set	NOUN
ejpam-3422	73	9	µt	µt	X
ejpam-3422	73	10	=	=	PUNCT
ejpam-3422	73	11	{	{	PUNCT
ejpam-3422	73	12	x	x	SYM
ejpam-3422	73	13	∈	∈	PROPN
ejpam-3422	73	14	m	m	PROPN
ejpam-3422	73	15	|µ(x	|µ(x	NOUN
ejpam-3422	73	16	)	)	PUNCT
ejpam-3422	73	17	≥	≥	PROPN
ejpam-3422	73	18	t	t	PROPN
ejpam-3422	73	19	}	}	PUNCT
ejpam-3422	73	20	is	be	AUX
ejpam-3422	73	21	a	a	DET
ejpam-3422	73	22	subset	subset	NOUN
ejpam-3422	73	23	of	of	ADP
ejpam-3422	73	24	m	m	PROPN
ejpam-3422	73	25	,	,	PUNCT
ejpam-3422	73	26	called	call	VERB
ejpam-3422	73	27	a	a	DET
ejpam-3422	73	28	level	level	NOUN
ejpam-3422	73	29	subset	subset	NOUN
ejpam-3422	73	30	of	of	ADP
ejpam-3422	73	31	µ.	µ.	PROPN
ejpam-3422	73	32	3	3	NUM
ejpam-3422	73	33	.	.	PUNCT
ejpam-3422	73	34	implicative	implicative	PROPN
ejpam-3422	73	35	hyper	hyper	ADJ
ejpam-3422	73	36	gr	gr	PROPN
ejpam-3422	73	37	-	-	PUNCT
ejpam-3422	73	38	ideals	ideal	NOUN
ejpam-3422	73	39	definition	definition	NOUN
ejpam-3422	73	40	3.1	3.1	NUM
ejpam-3422	73	41	.	.	PUNCT
ejpam-3422	74	1	a	a	DET
ejpam-3422	74	2	nonempty	nonempty	NOUN
ejpam-3422	74	3	subset	subset	VERB
ejpam-3422	74	4	i	i	PRON
ejpam-3422	74	5	of	of	ADP
ejpam-3422	74	6	a	a	DET
ejpam-3422	74	7	hyper	hyper	ADJ
ejpam-3422	74	8	gr	gr	NOUN
ejpam-3422	74	9	-	-	PUNCT
ejpam-3422	74	10	algebra	algebra	NOUN
ejpam-3422	74	11	h	h	NOUN
ejpam-3422	74	12	is	be	AUX
ejpam-3422	74	13	called	call	VERB
ejpam-3422	74	14	an	an	DET
ejpam-3422	74	15	implicative	implicative	ADJ
ejpam-3422	74	16	hyper	hyper	ADJ
ejpam-3422	74	17	gr	gr	NOUN
ejpam-3422	74	18	-	-	PUNCT
ejpam-3422	74	19	ideal	ideal	NOUN
ejpam-3422	74	20	of	of	ADP
ejpam-3422	74	21	h	h	NOUN
ejpam-3422	74	22	if	if	SCONJ
ejpam-3422	74	23	for	for	ADP
ejpam-3422	74	24	any	any	DET
ejpam-3422	74	25	x	x	NOUN
ejpam-3422	74	26	,	,	PUNCT
ejpam-3422	74	27	y	y	PROPN
ejpam-3422	74	28	,	,	PUNCT
ejpam-3422	74	29	z	z	PROPN
ejpam-3422	74	30	∈	∈	PROPN
ejpam-3422	74	31	h	h	NOUN
ejpam-3422	74	32	(	(	PUNCT
ejpam-3422	74	33	ih1	ih1	NOUN
ejpam-3422	74	34	)	)	PUNCT
ejpam-3422	74	35	0	0	PUNCT
ejpam-3422	75	1	∈	∈	PROPN
ejpam-3422	75	2	i	i	PRON
ejpam-3422	75	3	,	,	PUNCT
ejpam-3422	75	4	and	and	CCONJ
ejpam-3422	75	5	(	(	PUNCT
ejpam-3422	75	6	ih2	ih2	NOUN
ejpam-3422	75	7	)	)	PUNCT
ejpam-3422	75	8	(	(	PUNCT
ejpam-3422	75	9	x~	x~	PROPN
ejpam-3422	75	10	z	z	PROPN
ejpam-3422	75	11	)	)	PUNCT
ejpam-3422	75	12	~	~	PUNCT
ejpam-3422	75	13	(	(	PUNCT
ejpam-3422	75	14	y	y	X
ejpam-3422	75	15	~	~	PUNCT
ejpam-3422	75	16	x	x	X
ejpam-3422	75	17	)	)	PUNCT
ejpam-3422	75	18	⊆	⊆	NUM
ejpam-3422	75	19	i	i	PROPN
ejpam-3422	75	20	and	and	CCONJ
ejpam-3422	75	21	z	z	NOUN
ejpam-3422	75	22	∈	∈	PROPN
ejpam-3422	76	1	i	i	PRON
ejpam-3422	76	2	imply	imply	VERB
ejpam-3422	76	3	x	x	X
ejpam-3422	76	4	∈	∈	PROPN
ejpam-3422	76	5	i.	i.	PROPN
ejpam-3422	76	6	a.	a.	PROPN
ejpam-3422	76	7	macodi	macodi	PROPN
ejpam-3422	76	8	-	-	PUNCT
ejpam-3422	76	9	ringia	ringia	ADJ
ejpam-3422	76	10	,	,	PUNCT
ejpam-3422	76	11	g.	g.	PROPN
ejpam-3422	76	12	petalcorin	petalcorin	PROPN
ejpam-3422	76	13	,	,	PUNCT
ejpam-3422	76	14	jr	jr	PROPN
ejpam-3422	76	15	.	.	PROPN
ejpam-3422	76	16	/	/	SYM
ejpam-3422	76	17	eur	eur	PROPN
ejpam-3422	76	18	.	.	PUNCT
ejpam-3422	77	1	j.	j.	PROPN
ejpam-3422	77	2	pure	pure	PROPN
ejpam-3422	77	3	appl	appl	PROPN
ejpam-3422	77	4	.	.	PROPN
ejpam-3422	77	5	math	math	PROPN
ejpam-3422	77	6	,	,	PUNCT
ejpam-3422	77	7	12	12	NUM
ejpam-3422	77	8	(	(	PUNCT
ejpam-3422	77	9	2	2	NUM
ejpam-3422	77	10	)	)	PUNCT
ejpam-3422	77	11	(	(	PUNCT
ejpam-3422	77	12	2019	2019	NUM
ejpam-3422	77	13	)	)	PUNCT
ejpam-3422	77	14	,	,	PUNCT
ejpam-3422	77	15	409	409	NUM
ejpam-3422	77	16	-	-	SYM
ejpam-3422	77	17	417	417	NUM
ejpam-3422	77	18	412	412	NUM
ejpam-3422	77	19	example	example	NOUN
ejpam-3422	77	20	3.2	3.2	NUM
ejpam-3422	77	21	.	.	PUNCT
ejpam-3422	78	1	consider	consider	VERB
ejpam-3422	78	2	a	a	DET
ejpam-3422	78	3	set	set	NOUN
ejpam-3422	78	4	h	h	NOUN
ejpam-3422	78	5	=	=	SYM
ejpam-3422	78	6	{	{	PUNCT
ejpam-3422	78	7	0	0	NUM
ejpam-3422	78	8	,	,	PUNCT
ejpam-3422	78	9	1	1	NUM
ejpam-3422	78	10	,	,	PUNCT
ejpam-3422	78	11	2	2	NUM
ejpam-3422	78	12	,	,	PUNCT
ejpam-3422	78	13	3	3	NUM
ejpam-3422	78	14	}	}	PUNCT
ejpam-3422	78	15	with	with	ADP
ejpam-3422	78	16	the	the	DET
ejpam-3422	78	17	cayley	cayley	ADJ
ejpam-3422	78	18	table	table	NOUN
ejpam-3422	78	19	below	below	ADV
ejpam-3422	78	20	.	.	PUNCT
ejpam-3422	79	1	~	~	PUNCT
ejpam-3422	79	2	0	0	NUM
ejpam-3422	80	1	1	1	NUM
ejpam-3422	80	2	2	2	NUM
ejpam-3422	80	3	3	3	NUM
ejpam-3422	80	4	0	0	NUM
ejpam-3422	80	5	{	{	PUNCT
ejpam-3422	80	6	0	0	NUM
ejpam-3422	80	7	,	,	PUNCT
ejpam-3422	80	8	1	1	NUM
ejpam-3422	80	9	,	,	PUNCT
ejpam-3422	80	10	3	3	NUM
ejpam-3422	80	11	}	}	PUNCT
ejpam-3422	80	12	{	{	PUNCT
ejpam-3422	80	13	0	0	NUM
ejpam-3422	80	14	,	,	PUNCT
ejpam-3422	80	15	1	1	NUM
ejpam-3422	80	16	,	,	PUNCT
ejpam-3422	80	17	3	3	NUM
ejpam-3422	80	18	}	}	PUNCT
ejpam-3422	80	19	{	{	PUNCT
ejpam-3422	80	20	0	0	NUM
ejpam-3422	80	21	,	,	PUNCT
ejpam-3422	80	22	1	1	NUM
ejpam-3422	80	23	,	,	PUNCT
ejpam-3422	80	24	3	3	NUM
ejpam-3422	80	25	}	}	PUNCT
ejpam-3422	80	26	{	{	PUNCT
ejpam-3422	80	27	0	0	NUM
ejpam-3422	80	28	,	,	PUNCT
ejpam-3422	80	29	1	1	NUM
ejpam-3422	80	30	,	,	PUNCT
ejpam-3422	80	31	3	3	NUM
ejpam-3422	80	32	}	}	SYM
ejpam-3422	80	33	1	1	NUM
ejpam-3422	80	34	{	{	PUNCT
ejpam-3422	80	35	0	0	NUM
ejpam-3422	80	36	,	,	PUNCT
ejpam-3422	80	37	1	1	NUM
ejpam-3422	80	38	,	,	PUNCT
ejpam-3422	80	39	3	3	NUM
ejpam-3422	80	40	}	}	PUNCT
ejpam-3422	80	41	{	{	PUNCT
ejpam-3422	80	42	0	0	NUM
ejpam-3422	80	43	,	,	PUNCT
ejpam-3422	80	44	1	1	NUM
ejpam-3422	80	45	,	,	PUNCT
ejpam-3422	80	46	3	3	NUM
ejpam-3422	80	47	}	}	PUNCT
ejpam-3422	80	48	{	{	PUNCT
ejpam-3422	80	49	0	0	NUM
ejpam-3422	80	50	,	,	PUNCT
ejpam-3422	80	51	1	1	NUM
ejpam-3422	80	52	,	,	PUNCT
ejpam-3422	80	53	3	3	NUM
ejpam-3422	80	54	}	}	PUNCT
ejpam-3422	80	55	{	{	PUNCT
ejpam-3422	80	56	0	0	NUM
ejpam-3422	80	57	,	,	PUNCT
ejpam-3422	80	58	1	1	NUM
ejpam-3422	80	59	,	,	PUNCT
ejpam-3422	80	60	3	3	NUM
ejpam-3422	80	61	}	}	SYM
ejpam-3422	80	62	2	2	NUM
ejpam-3422	80	63	{	{	PUNCT
ejpam-3422	80	64	0	0	NUM
ejpam-3422	80	65	,	,	PUNCT
ejpam-3422	80	66	1	1	NUM
ejpam-3422	80	67	,	,	PUNCT
ejpam-3422	80	68	3	3	NUM
ejpam-3422	80	69	}	}	PUNCT
ejpam-3422	80	70	{	{	PUNCT
ejpam-3422	80	71	0	0	NUM
ejpam-3422	80	72	,	,	PUNCT
ejpam-3422	80	73	1	1	NUM
ejpam-3422	80	74	}	}	PUNCT
ejpam-3422	80	75	{	{	PUNCT
ejpam-3422	80	76	0	0	NUM
ejpam-3422	80	77	,	,	PUNCT
ejpam-3422	80	78	1	1	NUM
ejpam-3422	80	79	}	}	PUNCT
ejpam-3422	80	80	{	{	PUNCT
ejpam-3422	80	81	3	3	NUM
ejpam-3422	80	82	}	}	SYM
ejpam-3422	80	83	3	3	NUM
ejpam-3422	80	84	{	{	PUNCT
ejpam-3422	80	85	0	0	NUM
ejpam-3422	80	86	,	,	PUNCT
ejpam-3422	80	87	1	1	NUM
ejpam-3422	80	88	,	,	PUNCT
ejpam-3422	80	89	3	3	NUM
ejpam-3422	80	90	}	}	PUNCT
ejpam-3422	80	91	{	{	PUNCT
ejpam-3422	80	92	0	0	NUM
ejpam-3422	80	93	,	,	PUNCT
ejpam-3422	80	94	1	1	NUM
ejpam-3422	80	95	,	,	PUNCT
ejpam-3422	80	96	3	3	NUM
ejpam-3422	80	97	}	}	PUNCT
ejpam-3422	80	98	{	{	PUNCT
ejpam-3422	80	99	0	0	NUM
ejpam-3422	80	100	,	,	PUNCT
ejpam-3422	80	101	1	1	NUM
ejpam-3422	80	102	,	,	PUNCT
ejpam-3422	80	103	3	3	NUM
ejpam-3422	80	104	}	}	PUNCT
ejpam-3422	80	105	{	{	PUNCT
ejpam-3422	80	106	0	0	NUM
ejpam-3422	80	107	}	}	PUNCT
ejpam-3422	80	108	it	it	PRON
ejpam-3422	80	109	can	can	AUX
ejpam-3422	80	110	be	be	AUX
ejpam-3422	80	111	shown	show	VERB
ejpam-3422	80	112	that	that	SCONJ
ejpam-3422	80	113	h	h	NOUN
ejpam-3422	80	114	is	be	AUX
ejpam-3422	80	115	a	a	DET
ejpam-3422	80	116	hyper	hyper	ADJ
ejpam-3422	80	117	gr	gr	NOUN
ejpam-3422	80	118	-	-	NOUN
ejpam-3422	80	119	algebra	algebra	NOUN
ejpam-3422	80	120	.	.	PUNCT
ejpam-3422	81	1	by	by	ADP
ejpam-3422	81	2	routine	routine	ADJ
ejpam-3422	81	3	calculations	calculation	NOUN
ejpam-3422	81	4	,	,	PUNCT
ejpam-3422	81	5	we	we	PRON
ejpam-3422	81	6	can	can	AUX
ejpam-3422	81	7	see	see	VERB
ejpam-3422	81	8	that	that	SCONJ
ejpam-3422	81	9	the	the	DET
ejpam-3422	81	10	following	follow	VERB
ejpam-3422	81	11	are	be	AUX
ejpam-3422	81	12	true	true	ADJ
ejpam-3422	81	13	:	:	PUNCT
ejpam-3422	81	14	(	(	PUNCT
ejpam-3422	81	15	i	i	NOUN
ejpam-3422	81	16	)	)	PUNCT
ejpam-3422	81	17	h	h	NOUN
ejpam-3422	81	18	,	,	PUNCT
ejpam-3422	81	19	{	{	PUNCT
ejpam-3422	81	20	0	0	NUM
ejpam-3422	81	21	}	}	PUNCT
ejpam-3422	81	22	,	,	PUNCT
ejpam-3422	81	23	{	{	PUNCT
ejpam-3422	81	24	0	0	NUM
ejpam-3422	81	25	,	,	PUNCT
ejpam-3422	81	26	1	1	NUM
ejpam-3422	81	27	}	}	PUNCT
ejpam-3422	81	28	,	,	PUNCT
ejpam-3422	81	29	{	{	PUNCT
ejpam-3422	81	30	0	0	NUM
ejpam-3422	81	31	,	,	PUNCT
ejpam-3422	81	32	2	2	NUM
ejpam-3422	81	33	}	}	PUNCT
ejpam-3422	81	34	,	,	PUNCT
ejpam-3422	81	35	{	{	PUNCT
ejpam-3422	81	36	0	0	NUM
ejpam-3422	81	37	,	,	PUNCT
ejpam-3422	81	38	3	3	NUM
ejpam-3422	81	39	}	}	PUNCT
ejpam-3422	81	40	,	,	PUNCT
ejpam-3422	81	41	{	{	PUNCT
ejpam-3422	81	42	0	0	NUM
ejpam-3422	81	43	,	,	PUNCT
ejpam-3422	81	44	2	2	NUM
ejpam-3422	81	45	,	,	PUNCT
ejpam-3422	81	46	3	3	NUM
ejpam-3422	81	47	}	}	PUNCT
ejpam-3422	81	48	,	,	PUNCT
ejpam-3422	81	49	and	and	CCONJ
ejpam-3422	81	50	{	{	PUNCT
ejpam-3422	81	51	0	0	NUM
ejpam-3422	81	52	,	,	PUNCT
ejpam-3422	81	53	1	1	NUM
ejpam-3422	81	54	,	,	PUNCT
ejpam-3422	81	55	2	2	NUM
ejpam-3422	81	56	}	}	PUNCT
ejpam-3422	81	57	are	be	AUX
ejpam-3422	81	58	the	the	DET
ejpam-3422	81	59	only	only	ADJ
ejpam-3422	81	60	implicative	implicative	ADJ
ejpam-3422	81	61	hyper	hyper	ADJ
ejpam-3422	81	62	grideals	grideal	NOUN
ejpam-3422	81	63	of	of	ADP
ejpam-3422	81	64	h	h	NOUN
ejpam-3422	81	65	;	;	PUNCT
ejpam-3422	81	66	and	and	CCONJ
ejpam-3422	81	67	(	(	PUNCT
ejpam-3422	81	68	ii	ii	NOUN
ejpam-3422	81	69	)	)	PUNCT
ejpam-3422	81	70	h	h	NOUN
ejpam-3422	81	71	,	,	PUNCT
ejpam-3422	81	72	{	{	PUNCT
ejpam-3422	81	73	0	0	NUM
ejpam-3422	81	74	}	}	PUNCT
ejpam-3422	81	75	,	,	PUNCT
ejpam-3422	81	76	{	{	PUNCT
ejpam-3422	81	77	0	0	NUM
ejpam-3422	81	78	,	,	PUNCT
ejpam-3422	81	79	1	1	NUM
ejpam-3422	81	80	,	,	PUNCT
ejpam-3422	81	81	2	2	NUM
ejpam-3422	81	82	}	}	PUNCT
ejpam-3422	81	83	,	,	PUNCT
ejpam-3422	81	84	and	and	CCONJ
ejpam-3422	81	85	{	{	PUNCT
ejpam-3422	81	86	0	0	NUM
ejpam-3422	81	87	,	,	PUNCT
ejpam-3422	81	88	2	2	NUM
ejpam-3422	81	89	}	}	PUNCT
ejpam-3422	81	90	are	be	AUX
ejpam-3422	81	91	the	the	DET
ejpam-3422	81	92	only	only	ADJ
ejpam-3422	81	93	hyper	hyper	ADJ
ejpam-3422	81	94	gr	gr	NOUN
ejpam-3422	81	95	-	-	PUNCT
ejpam-3422	81	96	ideals	ideal	NOUN
ejpam-3422	81	97	of	of	ADP
ejpam-3422	81	98	h.	h.	PROPN
ejpam-3422	81	99	moreover	moreover	ADV
ejpam-3422	81	100	,	,	PUNCT
ejpam-3422	81	101	since	since	SCONJ
ejpam-3422	81	102	2~1	2~1	NUM
ejpam-3422	81	103	=	=	SYM
ejpam-3422	81	104	{	{	PUNCT
ejpam-3422	81	105	0	0	NUM
ejpam-3422	81	106	,	,	PUNCT
ejpam-3422	81	107	1	1	NUM
ejpam-3422	81	108	}	}	PUNCT
ejpam-3422	81	109	and	and	CCONJ
ejpam-3422	81	110	1	1	NUM
ejpam-3422	81	111	∈	∈	NOUN
ejpam-3422	81	112	{	{	PUNCT
ejpam-3422	81	113	0	0	NUM
ejpam-3422	81	114	,	,	PUNCT
ejpam-3422	81	115	1	1	NUM
ejpam-3422	81	116	}	}	PUNCT
ejpam-3422	81	117	but	but	CCONJ
ejpam-3422	81	118	2	2	NUM
ejpam-3422	81	119	/∈	/∈	PUNCT
ejpam-3422	81	120	{	{	PUNCT
ejpam-3422	81	121	0	0	NUM
ejpam-3422	81	122	,	,	PUNCT
ejpam-3422	81	123	1	1	NUM
ejpam-3422	81	124	}	}	PUNCT
ejpam-3422	81	125	,	,	PUNCT
ejpam-3422	81	126	{	{	PUNCT
ejpam-3422	81	127	0	0	NUM
ejpam-3422	81	128	,	,	PUNCT
ejpam-3422	81	129	1	1	NUM
ejpam-3422	81	130	}	}	PUNCT
ejpam-3422	81	131	is	be	AUX
ejpam-3422	81	132	not	not	PART
ejpam-3422	81	133	a	a	DET
ejpam-3422	81	134	hyper	hyper	ADJ
ejpam-3422	81	135	gr	gr	NOUN
ejpam-3422	81	136	-	-	PUNCT
ejpam-3422	81	137	ideal	ideal	NOUN
ejpam-3422	81	138	of	of	ADP
ejpam-3422	81	139	h.	h.	PROPN
ejpam-3422	81	140	furthermore	furthermore	ADV
ejpam-3422	81	141	,	,	PUNCT
ejpam-3422	81	142	note	note	VERB
ejpam-3422	81	143	that	that	SCONJ
ejpam-3422	81	144	(	(	PUNCT
ejpam-3422	81	145	2~0)~	2~0)~	NUM
ejpam-3422	81	146	(	(	PUNCT
ejpam-3422	81	147	0~2	0~2	NUM
ejpam-3422	81	148	)	)	PUNCT
ejpam-3422	81	149	=	=	PRON
ejpam-3422	81	150	{	{	PUNCT
ejpam-3422	81	151	0	0	NUM
ejpam-3422	81	152	,	,	PUNCT
ejpam-3422	81	153	1	1	NUM
ejpam-3422	81	154	,	,	PUNCT
ejpam-3422	81	155	3	3	NUM
ejpam-3422	81	156	}	}	PUNCT
ejpam-3422	81	157	and	and	CCONJ
ejpam-3422	81	158	0	0	NUM
ejpam-3422	81	159	∈	∈	NOUN
ejpam-3422	81	160	{	{	PUNCT
ejpam-3422	81	161	0	0	NUM
ejpam-3422	81	162	,	,	PUNCT
ejpam-3422	81	163	1	1	NUM
ejpam-3422	81	164	,	,	PUNCT
ejpam-3422	81	165	3	3	NUM
ejpam-3422	81	166	}	}	PUNCT
ejpam-3422	81	167	but	but	CCONJ
ejpam-3422	81	168	2	2	NUM
ejpam-3422	81	169	/∈	/∈	PUNCT
ejpam-3422	81	170	{	{	PUNCT
ejpam-3422	81	171	0	0	NUM
ejpam-3422	81	172	,	,	PUNCT
ejpam-3422	81	173	1	1	NUM
ejpam-3422	81	174	,	,	PUNCT
ejpam-3422	81	175	3	3	NUM
ejpam-3422	81	176	}	}	PUNCT
ejpam-3422	81	177	and	and	CCONJ
ejpam-3422	81	178	so	so	ADV
ejpam-3422	81	179	{	{	PUNCT
ejpam-3422	81	180	0	0	NUM
ejpam-3422	81	181	,	,	PUNCT
ejpam-3422	81	182	1	1	NUM
ejpam-3422	81	183	,	,	PUNCT
ejpam-3422	81	184	3	3	NUM
ejpam-3422	81	185	}	}	PUNCT
ejpam-3422	81	186	is	be	AUX
ejpam-3422	81	187	not	not	PART
ejpam-3422	81	188	an	an	DET
ejpam-3422	81	189	implicative	implicative	ADJ
ejpam-3422	81	190	hyper	hyper	ADJ
ejpam-3422	81	191	gr	gr	NOUN
ejpam-3422	81	192	-	-	PUNCT
ejpam-3422	81	193	ideal	ideal	NOUN
ejpam-3422	81	194	of	of	ADP
ejpam-3422	81	195	h.	h.	PROPN
ejpam-3422	81	196	remark	remark	PROPN
ejpam-3422	81	197	3.3	3.3	NUM
ejpam-3422	81	198	.	.	PUNCT
ejpam-3422	82	1	example	example	NOUN
ejpam-3422	82	2	3.2	3.2	NUM
ejpam-3422	82	3	shows	show	VERB
ejpam-3422	82	4	that	that	SCONJ
ejpam-3422	82	5	not	not	PART
ejpam-3422	82	6	all	all	DET
ejpam-3422	82	7	implicative	implicative	ADJ
ejpam-3422	82	8	hyper	hyper	ADJ
ejpam-3422	82	9	gr	gr	NOUN
ejpam-3422	82	10	-	-	PUNCT
ejpam-3422	82	11	ideals	ideal	NOUN
ejpam-3422	82	12	are	be	AUX
ejpam-3422	82	13	hyper	hyper	ADJ
ejpam-3422	82	14	grideals	grideal	NOUN
ejpam-3422	82	15	.	.	PUNCT
ejpam-3422	83	1	moreover	moreover	ADV
ejpam-3422	83	2	,	,	PUNCT
ejpam-3422	83	3	h	h	NOUN
ejpam-3422	83	4	in	in	ADP
ejpam-3422	83	5	example	example	NOUN
ejpam-3422	83	6	3.2	3.2	NUM
ejpam-3422	83	7	is	be	AUX
ejpam-3422	83	8	not	not	PART
ejpam-3422	83	9	a	a	DET
ejpam-3422	83	10	hyper	hyper	ADJ
ejpam-3422	83	11	bci	bci	NOUN
ejpam-3422	83	12	-	-	NOUN
ejpam-3422	83	13	algebra	algebra	NOUN
ejpam-3422	83	14	since	since	SCONJ
ejpam-3422	83	15	2	2	NUM
ejpam-3422	83	16	�	�	PROPN
ejpam-3422	83	17	1	1	NUM
ejpam-3422	83	18	and	and	CCONJ
ejpam-3422	83	19	1	1	NUM
ejpam-3422	83	20	�	�	PROPN
ejpam-3422	83	21	2	2	NUM
ejpam-3422	83	22	but	but	CCONJ
ejpam-3422	83	23	2	2	NUM
ejpam-3422	83	24	6=	6=	SYM
ejpam-3422	83	25	1	1	NUM
ejpam-3422	83	26	.	.	PUNCT
ejpam-3422	84	1	this	this	PRON
ejpam-3422	84	2	shows	show	VERB
ejpam-3422	84	3	that	that	SCONJ
ejpam-3422	84	4	implicative	implicative	ADJ
ejpam-3422	84	5	hyper	hyper	ADJ
ejpam-3422	84	6	gr	gr	NOUN
ejpam-3422	84	7	-	-	PUNCT
ejpam-3422	84	8	ideals	ideal	NOUN
ejpam-3422	84	9	and	and	CCONJ
ejpam-3422	84	10	weak	weak	ADJ
ejpam-3422	84	11	implicative	implicative	ADJ
ejpam-3422	84	12	hyper	hyper	ADJ
ejpam-3422	84	13	bck	bck	NOUN
ejpam-3422	84	14	-	-	PUNCT
ejpam-3422	84	15	ideals	ideal	NOUN
ejpam-3422	84	16	are	be	AUX
ejpam-3422	84	17	not	not	PART
ejpam-3422	84	18	equivalent	equivalent	ADJ
ejpam-3422	84	19	.	.	PUNCT
ejpam-3422	85	1	example	example	NOUN
ejpam-3422	85	2	3.4	3.4	NUM
ejpam-3422	85	3	.	.	PUNCT
ejpam-3422	86	1	consider	consider	VERB
ejpam-3422	86	2	a	a	DET
ejpam-3422	86	3	set	set	NOUN
ejpam-3422	86	4	h	h	NOUN
ejpam-3422	86	5	=	=	SYM
ejpam-3422	86	6	{	{	PUNCT
ejpam-3422	86	7	0	0	NUM
ejpam-3422	86	8	,	,	PUNCT
ejpam-3422	86	9	1	1	NUM
ejpam-3422	86	10	,	,	PUNCT
ejpam-3422	86	11	2	2	NUM
ejpam-3422	86	12	}	}	PUNCT
ejpam-3422	86	13	with	with	ADP
ejpam-3422	86	14	the	the	DET
ejpam-3422	86	15	cayley	cayley	ADJ
ejpam-3422	86	16	table	table	NOUN
ejpam-3422	86	17	below	below	ADV
ejpam-3422	86	18	.	.	PUNCT
ejpam-3422	87	1	~	~	PUNCT
ejpam-3422	87	2	0	0	NUM
ejpam-3422	88	1	1	1	NUM
ejpam-3422	88	2	2	2	NUM
ejpam-3422	88	3	0	0	NUM
ejpam-3422	88	4	{	{	PUNCT
ejpam-3422	88	5	0	0	NUM
ejpam-3422	88	6	}	}	PUNCT
ejpam-3422	88	7	{	{	PUNCT
ejpam-3422	88	8	0	0	NUM
ejpam-3422	88	9	}	}	PUNCT
ejpam-3422	88	10	{	{	PUNCT
ejpam-3422	88	11	0	0	NUM
ejpam-3422	88	12	}	}	SYM
ejpam-3422	88	13	1	1	NUM
ejpam-3422	88	14	{	{	PUNCT
ejpam-3422	88	15	0	0	NUM
ejpam-3422	88	16	}	}	PUNCT
ejpam-3422	88	17	{	{	PUNCT
ejpam-3422	88	18	0	0	NUM
ejpam-3422	88	19	}	}	PUNCT
ejpam-3422	88	20	{	{	PUNCT
ejpam-3422	88	21	1	1	NUM
ejpam-3422	88	22	}	}	SYM
ejpam-3422	88	23	2	2	NUM
ejpam-3422	88	24	{	{	PUNCT
ejpam-3422	88	25	0	0	NUM
ejpam-3422	88	26	,	,	PUNCT
ejpam-3422	88	27	2	2	NUM
ejpam-3422	88	28	}	}	PUNCT
ejpam-3422	88	29	{	{	PUNCT
ejpam-3422	88	30	2	2	NUM
ejpam-3422	88	31	}	}	PUNCT
ejpam-3422	88	32	{	{	PUNCT
ejpam-3422	88	33	0	0	NUM
ejpam-3422	88	34	}	}	PUNCT
ejpam-3422	88	35	it	it	PRON
ejpam-3422	88	36	can	can	AUX
ejpam-3422	88	37	be	be	AUX
ejpam-3422	88	38	verified	verify	VERB
ejpam-3422	88	39	that	that	SCONJ
ejpam-3422	88	40	h	h	NOUN
ejpam-3422	88	41	is	be	AUX
ejpam-3422	88	42	a	a	DET
ejpam-3422	88	43	hyper	hyper	ADJ
ejpam-3422	88	44	gr	gr	NOUN
ejpam-3422	88	45	-	-	NOUN
ejpam-3422	88	46	algebra	algebra	NOUN
ejpam-3422	88	47	.	.	PUNCT
ejpam-3422	89	1	since	since	SCONJ
ejpam-3422	89	2	(	(	PUNCT
ejpam-3422	89	3	1~	1~	NUM
ejpam-3422	89	4	0)~	0)~	NOUN
ejpam-3422	89	5	(	(	PUNCT
ejpam-3422	89	6	0~	0~	NOUN
ejpam-3422	89	7	1	1	NUM
ejpam-3422	89	8	)	)	PUNCT
ejpam-3422	89	9	=	=	PRON
ejpam-3422	89	10	{	{	PUNCT
ejpam-3422	89	11	0	0	NUM
ejpam-3422	89	12	}	}	PUNCT
ejpam-3422	89	13	and	and	CCONJ
ejpam-3422	89	14	0	0	NUM
ejpam-3422	89	15	∈	∈	NOUN
ejpam-3422	89	16	{	{	PUNCT
ejpam-3422	89	17	0	0	NUM
ejpam-3422	89	18	}	}	PUNCT
ejpam-3422	89	19	but	but	CCONJ
ejpam-3422	89	20	1	1	NUM
ejpam-3422	89	21	6=	6=	NUM
ejpam-3422	89	22	{	{	PUNCT
ejpam-3422	89	23	0	0	NUM
ejpam-3422	89	24	}	}	PUNCT
ejpam-3422	89	25	,	,	PUNCT
ejpam-3422	89	26	{	{	PUNCT
ejpam-3422	89	27	0	0	X
ejpam-3422	89	28	}	}	PUNCT
ejpam-3422	89	29	is	be	AUX
ejpam-3422	89	30	not	not	PART
ejpam-3422	89	31	an	an	DET
ejpam-3422	89	32	implicative	implicative	ADJ
ejpam-3422	89	33	hyper	hyper	ADJ
ejpam-3422	89	34	gr	gr	NOUN
ejpam-3422	89	35	-	-	PUNCT
ejpam-3422	89	36	ideal	ideal	NOUN
ejpam-3422	89	37	of	of	ADP
ejpam-3422	89	38	h.	h.	PROPN
ejpam-3422	89	39	furthermore	furthermore	ADV
ejpam-3422	89	40	,	,	PUNCT
ejpam-3422	89	41	note	note	VERB
ejpam-3422	89	42	that	that	SCONJ
ejpam-3422	89	43	1~	1~	NUM
ejpam-3422	89	44	0	0	NUM
ejpam-3422	89	45	=	=	SYM
ejpam-3422	89	46	{	{	PUNCT
ejpam-3422	89	47	0	0	NUM
ejpam-3422	89	48	}	}	PUNCT
ejpam-3422	89	49	and	and	CCONJ
ejpam-3422	89	50	0	0	NUM
ejpam-3422	89	51	∈	∈	NOUN
ejpam-3422	89	52	{	{	PUNCT
ejpam-3422	89	53	0	0	NUM
ejpam-3422	89	54	}	}	PUNCT
ejpam-3422	89	55	but	but	CCONJ
ejpam-3422	89	56	1	1	NUM
ejpam-3422	89	57	/∈	/∈	PUNCT
ejpam-3422	89	58	{	{	PUNCT
ejpam-3422	89	59	0	0	NUM
ejpam-3422	89	60	}	}	PUNCT
ejpam-3422	89	61	.	.	PUNCT
ejpam-3422	90	1	this	this	PRON
ejpam-3422	90	2	implies	imply	VERB
ejpam-3422	90	3	that	that	SCONJ
ejpam-3422	90	4	{	{	PUNCT
ejpam-3422	90	5	0	0	X
ejpam-3422	90	6	}	}	PUNCT
ejpam-3422	90	7	is	be	AUX
ejpam-3422	90	8	not	not	PART
ejpam-3422	90	9	a	a	DET
ejpam-3422	90	10	hyper	hyper	ADJ
ejpam-3422	90	11	gr	gr	NOUN
ejpam-3422	90	12	-	-	PUNCT
ejpam-3422	90	13	ideal	ideal	NOUN
ejpam-3422	90	14	of	of	ADP
ejpam-3422	90	15	h.	h.	PROPN
ejpam-3422	90	16	remark	remark	PROPN
ejpam-3422	90	17	3.5	3.5	NUM
ejpam-3422	90	18	.	.	PUNCT
ejpam-3422	90	19	example	example	NOUN
ejpam-3422	90	20	3.4	3.4	NUM
ejpam-3422	90	21	shows	show	VERB
ejpam-3422	90	22	that	that	SCONJ
ejpam-3422	90	23	{	{	PUNCT
ejpam-3422	90	24	0	0	X
ejpam-3422	90	25	}	}	PUNCT
ejpam-3422	90	26	is	be	AUX
ejpam-3422	90	27	not	not	PART
ejpam-3422	90	28	always	always	ADV
ejpam-3422	90	29	an	an	DET
ejpam-3422	90	30	implicative	implicative	ADJ
ejpam-3422	90	31	hyper	hyper	ADJ
ejpam-3422	90	32	gr	gr	NOUN
ejpam-3422	90	33	-	-	PUNCT
ejpam-3422	90	34	ideal	ideal	NOUN
ejpam-3422	90	35	and	and	CCONJ
ejpam-3422	90	36	is	be	AUX
ejpam-3422	90	37	not	not	PART
ejpam-3422	90	38	always	always	ADV
ejpam-3422	90	39	a	a	DET
ejpam-3422	90	40	hyper	hyper	ADJ
ejpam-3422	90	41	gr	gr	NOUN
ejpam-3422	90	42	-	-	PUNCT
ejpam-3422	90	43	ideal	ideal	NOUN
ejpam-3422	90	44	of	of	ADP
ejpam-3422	90	45	a	a	DET
ejpam-3422	90	46	hyper	hyper	ADJ
ejpam-3422	90	47	gr	gr	NOUN
ejpam-3422	90	48	-	-	PUNCT
ejpam-3422	90	49	algebra	algebra	NOUN
ejpam-3422	90	50	h.	h.	NOUN
ejpam-3422	90	51	in	in	ADP
ejpam-3422	90	52	example	example	NOUN
ejpam-3422	90	53	3.4	3.4	NUM
ejpam-3422	90	54	,	,	PUNCT
ejpam-3422	90	55	we	we	PRON
ejpam-3422	90	56	can	can	AUX
ejpam-3422	90	57	see	see	VERB
ejpam-3422	90	58	that	that	PRON
ejpam-3422	90	59	1	1	NUM
ejpam-3422	90	60	/∈	/∈	NUM
ejpam-3422	90	61	1~	1~	NUM
ejpam-3422	90	62	0	0	PUNCT
ejpam-3422	90	63	and	and	CCONJ
ejpam-3422	90	64	not	not	PART
ejpam-3422	90	65	all	all	PRON
ejpam-3422	90	66	subset	subset	VERB
ejpam-3422	90	67	i	i	PRON
ejpam-3422	90	68	of	of	ADP
ejpam-3422	90	69	h	h	NOUN
ejpam-3422	90	70	containing	contain	VERB
ejpam-3422	90	71	0	0	NUM
ejpam-3422	90	72	is	be	AUX
ejpam-3422	90	73	an	an	DET
ejpam-3422	90	74	implicative	implicative	ADJ
ejpam-3422	90	75	hyper	hyper	ADJ
ejpam-3422	90	76	gr	gr	NOUN
ejpam-3422	90	77	-	-	PUNCT
ejpam-3422	90	78	ideal	ideal	NOUN
ejpam-3422	90	79	of	of	ADP
ejpam-3422	90	80	h.	h.	PROPN
ejpam-3422	90	81	example	example	PROPN
ejpam-3422	90	82	3.6	3.6	NUM
ejpam-3422	90	83	.	.	PUNCT
ejpam-3422	91	1	consider	consider	VERB
ejpam-3422	91	2	a	a	DET
ejpam-3422	91	3	set	set	NOUN
ejpam-3422	91	4	h	h	NOUN
ejpam-3422	91	5	=	=	SYM
ejpam-3422	91	6	{	{	PUNCT
ejpam-3422	91	7	0	0	NUM
ejpam-3422	91	8	,	,	PUNCT
ejpam-3422	91	9	1	1	NUM
ejpam-3422	91	10	,	,	PUNCT
ejpam-3422	91	11	2	2	NUM
ejpam-3422	91	12	}	}	PUNCT
ejpam-3422	91	13	with	with	ADP
ejpam-3422	91	14	the	the	DET
ejpam-3422	91	15	cayley	cayley	ADJ
ejpam-3422	91	16	table	table	NOUN
ejpam-3422	91	17	below	below	ADV
ejpam-3422	91	18	.	.	PUNCT
ejpam-3422	92	1	~	~	PUNCT
ejpam-3422	92	2	0	0	NUM
ejpam-3422	93	1	1	1	NUM
ejpam-3422	93	2	2	2	NUM
ejpam-3422	93	3	0	0	NUM
ejpam-3422	93	4	{	{	PUNCT
ejpam-3422	93	5	0	0	NUM
ejpam-3422	93	6	,	,	PUNCT
ejpam-3422	93	7	1	1	NUM
ejpam-3422	93	8	,	,	PUNCT
ejpam-3422	93	9	2	2	NUM
ejpam-3422	93	10	}	}	PUNCT
ejpam-3422	93	11	{	{	PUNCT
ejpam-3422	93	12	0	0	NUM
ejpam-3422	93	13	,	,	PUNCT
ejpam-3422	93	14	1	1	NUM
ejpam-3422	93	15	,	,	PUNCT
ejpam-3422	93	16	2	2	NUM
ejpam-3422	93	17	}	}	PUNCT
ejpam-3422	93	18	{	{	PUNCT
ejpam-3422	93	19	0	0	NUM
ejpam-3422	93	20	,	,	PUNCT
ejpam-3422	93	21	1	1	NUM
ejpam-3422	93	22	,	,	PUNCT
ejpam-3422	93	23	2	2	NUM
ejpam-3422	93	24	}	}	SYM
ejpam-3422	93	25	1	1	NUM
ejpam-3422	93	26	{	{	PUNCT
ejpam-3422	93	27	1	1	NUM
ejpam-3422	93	28	}	}	PUNCT
ejpam-3422	93	29	{	{	PUNCT
ejpam-3422	93	30	0	0	NUM
ejpam-3422	93	31	,	,	PUNCT
ejpam-3422	93	32	1	1	NUM
ejpam-3422	93	33	,	,	PUNCT
ejpam-3422	93	34	2	2	NUM
ejpam-3422	93	35	}	}	PUNCT
ejpam-3422	93	36	{	{	PUNCT
ejpam-3422	93	37	1	1	NUM
ejpam-3422	93	38	,	,	PUNCT
ejpam-3422	93	39	2	2	NUM
ejpam-3422	93	40	}	}	SYM
ejpam-3422	93	41	2	2	NUM
ejpam-3422	93	42	{	{	PUNCT
ejpam-3422	93	43	1	1	NUM
ejpam-3422	93	44	,	,	PUNCT
ejpam-3422	93	45	2	2	NUM
ejpam-3422	93	46	}	}	PUNCT
ejpam-3422	93	47	{	{	PUNCT
ejpam-3422	93	48	0	0	NUM
ejpam-3422	93	49	,	,	PUNCT
ejpam-3422	93	50	1	1	NUM
ejpam-3422	93	51	,	,	PUNCT
ejpam-3422	93	52	2	2	NUM
ejpam-3422	93	53	}	}	PUNCT
ejpam-3422	93	54	{	{	PUNCT
ejpam-3422	93	55	0	0	NUM
ejpam-3422	93	56	,	,	PUNCT
ejpam-3422	93	57	1	1	NUM
ejpam-3422	93	58	,	,	PUNCT
ejpam-3422	93	59	2	2	NUM
ejpam-3422	93	60	}	}	PUNCT
ejpam-3422	93	61	a.	a.	NOUN
ejpam-3422	93	62	macodi	macodi	NOUN
ejpam-3422	93	63	-	-	PUNCT
ejpam-3422	93	64	ringia	ringia	ADJ
ejpam-3422	93	65	,	,	PUNCT
ejpam-3422	93	66	g.	g.	PROPN
ejpam-3422	93	67	petalcorin	petalcorin	PROPN
ejpam-3422	93	68	,	,	PUNCT
ejpam-3422	93	69	jr	jr	PROPN
ejpam-3422	93	70	.	.	PROPN
ejpam-3422	93	71	/	/	SYM
ejpam-3422	93	72	eur	eur	PROPN
ejpam-3422	93	73	.	.	PUNCT
ejpam-3422	94	1	j.	j.	PROPN
ejpam-3422	94	2	pure	pure	PROPN
ejpam-3422	94	3	appl	appl	PROPN
ejpam-3422	94	4	.	.	PROPN
ejpam-3422	94	5	math	math	PROPN
ejpam-3422	94	6	,	,	PUNCT
ejpam-3422	94	7	12	12	NUM
ejpam-3422	94	8	(	(	PUNCT
ejpam-3422	94	9	2	2	NUM
ejpam-3422	94	10	)	)	PUNCT
ejpam-3422	94	11	(	(	PUNCT
ejpam-3422	94	12	2019	2019	NUM
ejpam-3422	94	13	)	)	PUNCT
ejpam-3422	94	14	,	,	PUNCT
ejpam-3422	94	15	409	409	NUM
ejpam-3422	94	16	-	-	SYM
ejpam-3422	94	17	417	417	NUM
ejpam-3422	94	18	413	413	NUM
ejpam-3422	94	19	it	it	PRON
ejpam-3422	94	20	can	can	AUX
ejpam-3422	94	21	be	be	AUX
ejpam-3422	94	22	verified	verify	VERB
ejpam-3422	94	23	that	that	SCONJ
ejpam-3422	94	24	h	h	NOUN
ejpam-3422	94	25	is	be	AUX
ejpam-3422	94	26	a	a	DET
ejpam-3422	94	27	hyper	hyper	ADJ
ejpam-3422	94	28	gr	gr	NOUN
ejpam-3422	94	29	-	-	NOUN
ejpam-3422	94	30	algebra	algebra	NOUN
ejpam-3422	94	31	.	.	PUNCT
ejpam-3422	95	1	clearly	clearly	ADV
ejpam-3422	95	2	,	,	PUNCT
ejpam-3422	95	3	x	x	X
ejpam-3422	95	4	∈	∈	NOUN
ejpam-3422	95	5	x	x	PUNCT
ejpam-3422	95	6	~	~	PUNCT
ejpam-3422	95	7	y	y	PROPN
ejpam-3422	95	8	for	for	ADP
ejpam-3422	95	9	all	all	DET
ejpam-3422	95	10	x	x	NOUN
ejpam-3422	95	11	,	,	PUNCT
ejpam-3422	95	12	y	y	PROPN
ejpam-3422	95	13	∈	∈	PROPN
ejpam-3422	95	14	h.	h.	PROPN
ejpam-3422	95	15	by	by	ADP
ejpam-3422	95	16	routine	routine	ADJ
ejpam-3422	95	17	calculations	calculation	NOUN
ejpam-3422	95	18	,	,	PUNCT
ejpam-3422	95	19	we	we	PRON
ejpam-3422	95	20	can	can	AUX
ejpam-3422	95	21	show	show	VERB
ejpam-3422	95	22	that	that	SCONJ
ejpam-3422	95	23	any	any	DET
ejpam-3422	95	24	subset	subset	NOUN
ejpam-3422	95	25	of	of	ADP
ejpam-3422	95	26	i	i	PRON
ejpam-3422	95	27	of	of	ADP
ejpam-3422	95	28	h	h	NOUN
ejpam-3422	95	29	containing	contain	VERB
ejpam-3422	95	30	0	0	NUM
ejpam-3422	95	31	is	be	AUX
ejpam-3422	95	32	an	an	DET
ejpam-3422	95	33	implicative	implicative	ADJ
ejpam-3422	95	34	hyper	hyper	ADJ
ejpam-3422	95	35	gr	gr	NOUN
ejpam-3422	95	36	-	-	PUNCT
ejpam-3422	95	37	ideal	ideal	NOUN
ejpam-3422	95	38	of	of	ADP
ejpam-3422	95	39	h.	h.	PROPN
ejpam-3422	95	40	the	the	DET
ejpam-3422	95	41	next	next	ADJ
ejpam-3422	95	42	proposition	proposition	NOUN
ejpam-3422	95	43	will	will	AUX
ejpam-3422	95	44	give	give	VERB
ejpam-3422	95	45	a	a	DET
ejpam-3422	95	46	generalization	generalization	NOUN
ejpam-3422	95	47	when	when	SCONJ
ejpam-3422	95	48	x	x	X
ejpam-3422	95	49	∈	∈	NOUN
ejpam-3422	95	50	x	x	PUNCT
ejpam-3422	95	51	~	~	PUNCT
ejpam-3422	95	52	y	y	PROPN
ejpam-3422	95	53	for	for	ADP
ejpam-3422	95	54	all	all	DET
ejpam-3422	95	55	x	x	PUNCT
ejpam-3422	95	56	and	and	CCONJ
ejpam-3422	95	57	y	y	PROPN
ejpam-3422	95	58	in	in	ADP
ejpam-3422	95	59	a	a	DET
ejpam-3422	95	60	hyper	hyper	ADJ
ejpam-3422	95	61	gr	gr	NOUN
ejpam-3422	95	62	-	-	PUNCT
ejpam-3422	95	63	algebra	algebra	NOUN
ejpam-3422	95	64	h.	h.	NOUN
ejpam-3422	95	65	proposition	proposition	NOUN
ejpam-3422	95	66	3.7	3.7	NUM
ejpam-3422	95	67	.	.	PUNCT
ejpam-3422	96	1	let	let	VERB
ejpam-3422	96	2	h	h	PRON
ejpam-3422	96	3	be	be	AUX
ejpam-3422	96	4	a	a	DET
ejpam-3422	96	5	hyper	hyper	ADJ
ejpam-3422	96	6	gr	gr	NOUN
ejpam-3422	96	7	-	-	PUNCT
ejpam-3422	96	8	algebra	algebra	NOUN
ejpam-3422	96	9	such	such	ADJ
ejpam-3422	96	10	that	that	SCONJ
ejpam-3422	96	11	x	x	SYM
ejpam-3422	96	12	∈	∈	NOUN
ejpam-3422	96	13	x	x	X
ejpam-3422	96	14	~	~	PUNCT
ejpam-3422	96	15	y	y	NOUN
ejpam-3422	96	16	for	for	ADP
ejpam-3422	96	17	any	any	DET
ejpam-3422	96	18	x	x	NOUN
ejpam-3422	96	19	,	,	PUNCT
ejpam-3422	96	20	y	y	PROPN
ejpam-3422	96	21	∈	∈	PROPN
ejpam-3422	96	22	h.	h.	NOUN
ejpam-3422	96	23	then	then	ADV
ejpam-3422	96	24	any	any	DET
ejpam-3422	96	25	subset	subset	NOUN
ejpam-3422	96	26	i	i	PRON
ejpam-3422	96	27	of	of	ADP
ejpam-3422	96	28	h	h	NOUN
ejpam-3422	96	29	containing	contain	VERB
ejpam-3422	96	30	0	0	NUM
ejpam-3422	96	31	is	be	AUX
ejpam-3422	96	32	an	an	DET
ejpam-3422	96	33	implicative	implicative	ADJ
ejpam-3422	96	34	hyper	hyper	ADJ
ejpam-3422	96	35	gr	gr	NOUN
ejpam-3422	96	36	-	-	PUNCT
ejpam-3422	96	37	ideal	ideal	NOUN
ejpam-3422	96	38	of	of	ADP
ejpam-3422	96	39	h.	h.	NOUN
ejpam-3422	96	40	proof	proof	NOUN
ejpam-3422	96	41	.	.	PUNCT
ejpam-3422	97	1	let	let	VERB
ejpam-3422	97	2	i	i	PRON
ejpam-3422	97	3	⊆	⊆	NUM
ejpam-3422	97	4	h	h	NOUN
ejpam-3422	97	5	and	and	CCONJ
ejpam-3422	97	6	0	0	NUM
ejpam-3422	97	7	∈	∈	PROPN
ejpam-3422	97	8	i.	i.	NOUN
ejpam-3422	97	9	let	let	VERB
ejpam-3422	97	10	x	x	PRON
ejpam-3422	97	11	,	,	PUNCT
ejpam-3422	97	12	y	y	PROPN
ejpam-3422	97	13	,	,	PUNCT
ejpam-3422	97	14	z	z	PROPN
ejpam-3422	97	15	∈	∈	PROPN
ejpam-3422	97	16	h	h	NOUN
ejpam-3422	97	17	such	such	ADJ
ejpam-3422	97	18	that	that	SCONJ
ejpam-3422	97	19	(	(	PUNCT
ejpam-3422	97	20	x	x	X
ejpam-3422	97	21	~	~	PUNCT
ejpam-3422	97	22	z	z	X
ejpam-3422	97	23	)	)	PUNCT
ejpam-3422	97	24	~	~	PUNCT
ejpam-3422	97	25	(	(	PUNCT
ejpam-3422	97	26	y	y	X
ejpam-3422	97	27	~	~	PUNCT
ejpam-3422	97	28	x	x	X
ejpam-3422	97	29	)	)	PUNCT
ejpam-3422	98	1	⊆	⊆	NUM
ejpam-3422	98	2	i	i	PROPN
ejpam-3422	98	3	and	and	CCONJ
ejpam-3422	98	4	z	z	PROPN
ejpam-3422	98	5	∈	∈	PROPN
ejpam-3422	98	6	i.	i.	NOUN
ejpam-3422	98	7	by	by	ADP
ejpam-3422	98	8	hypothesis	hypothesis	NOUN
ejpam-3422	98	9	,	,	PUNCT
ejpam-3422	98	10	x	x	PUNCT
ejpam-3422	98	11	∈	∈	PROPN
ejpam-3422	98	12	x~	x~	PROPN
ejpam-3422	98	13	z.	z.	PROPN
ejpam-3422	99	1	then	then	ADV
ejpam-3422	99	2	x~	x~	PROPN
ejpam-3422	99	3	w	w	PROPN
ejpam-3422	99	4	⊆	⊆	NUM
ejpam-3422	99	5	i	i	PRON
ejpam-3422	99	6	for	for	ADP
ejpam-3422	99	7	any	any	DET
ejpam-3422	99	8	w	w	PROPN
ejpam-3422	99	9	∈	∈	PROPN
ejpam-3422	99	10	y	y	PROPN
ejpam-3422	99	11	~	~	PUNCT
ejpam-3422	99	12	x.	x.	NOUN
ejpam-3422	99	13	it	it	PRON
ejpam-3422	99	14	follows	follow	VERB
ejpam-3422	99	15	from	from	ADP
ejpam-3422	99	16	the	the	DET
ejpam-3422	99	17	hypothesis	hypothesis	NOUN
ejpam-3422	99	18	that	that	PRON
ejpam-3422	99	19	x	x	PUNCT
ejpam-3422	99	20	∈	∈	PROPN
ejpam-3422	99	21	x~	x~	PROPN
ejpam-3422	99	22	w	w	PROPN
ejpam-3422	99	23	⊆	⊆	NUM
ejpam-3422	99	24	i.	i.	NOUN
ejpam-3422	99	25	hence	hence	ADV
ejpam-3422	99	26	,	,	PUNCT
ejpam-3422	99	27	i	i	PRON
ejpam-3422	99	28	is	be	AUX
ejpam-3422	99	29	an	an	DET
ejpam-3422	99	30	implicative	implicative	ADJ
ejpam-3422	99	31	hyper	hyper	ADJ
ejpam-3422	99	32	gr	gr	NOUN
ejpam-3422	99	33	-	-	PUNCT
ejpam-3422	99	34	ideal	ideal	NOUN
ejpam-3422	99	35	of	of	ADP
ejpam-3422	99	36	h.	h.	PROPN
ejpam-3422	99	37	lemma	lemma	PROPN
ejpam-3422	99	38	3.8	3.8	NUM
ejpam-3422	99	39	.	.	PUNCT
ejpam-3422	100	1	if	if	SCONJ
ejpam-3422	100	2	i	i	PRON
ejpam-3422	100	3	is	be	AUX
ejpam-3422	100	4	a	a	DET
ejpam-3422	100	5	hyper	hyper	ADJ
ejpam-3422	100	6	gr	gr	NOUN
ejpam-3422	100	7	-	-	PUNCT
ejpam-3422	100	8	ideal	ideal	NOUN
ejpam-3422	100	9	of	of	ADP
ejpam-3422	100	10	a	a	DET
ejpam-3422	100	11	hyper	hyper	ADJ
ejpam-3422	100	12	gr	gr	NOUN
ejpam-3422	100	13	-	-	PUNCT
ejpam-3422	100	14	algebra	algebra	NOUN
ejpam-3422	100	15	h	h	NOUN
ejpam-3422	100	16	,	,	PUNCT
ejpam-3422	100	17	then	then	ADV
ejpam-3422	100	18	a	a	DET
ejpam-3422	100	19	~	~	PUNCT
ejpam-3422	100	20	b	b	X
ejpam-3422	100	21	⊆	⊆	NUM
ejpam-3422	100	22	i	i	PROPN
ejpam-3422	100	23	and	and	CCONJ
ejpam-3422	100	24	b	b	NOUN
ejpam-3422	100	25	⊆	⊆	X
ejpam-3422	100	26	i	i	PRON
ejpam-3422	100	27	imply	imply	VERB
ejpam-3422	100	28	a	a	DET
ejpam-3422	100	29	⊆	⊆	NUM
ejpam-3422	100	30	i.	i.	NOUN
ejpam-3422	100	31	proof	proof	NOUN
ejpam-3422	100	32	.	.	PUNCT
ejpam-3422	101	1	suppose	suppose	VERB
ejpam-3422	101	2	a	a	PRON
ejpam-3422	101	3	~	~	PUNCT
ejpam-3422	101	4	b	b	X
ejpam-3422	101	5	⊆	⊆	NUM
ejpam-3422	101	6	i	i	PROPN
ejpam-3422	101	7	and	and	CCONJ
ejpam-3422	101	8	b	b	PROPN
ejpam-3422	101	9	⊆	⊆	NUM
ejpam-3422	101	10	i.	i.	NOUN
ejpam-3422	101	11	let	let	VERB
ejpam-3422	101	12	a	a	DET
ejpam-3422	101	13	∈	∈	NOUN
ejpam-3422	101	14	a.	a.	NOUN
ejpam-3422	101	15	then	then	ADV
ejpam-3422	101	16	a	a	PRON
ejpam-3422	101	17	~	~	PUNCT
ejpam-3422	101	18	b	b	X
ejpam-3422	101	19	⊆	⊆	NUM
ejpam-3422	101	20	i	i	PRON
ejpam-3422	101	21	for	for	ADP
ejpam-3422	101	22	any	any	DET
ejpam-3422	101	23	b	b	PROPN
ejpam-3422	101	24	∈	∈	PROPN
ejpam-3422	101	25	b.	b.	PROPN
ejpam-3422	101	26	since	since	SCONJ
ejpam-3422	101	27	i	i	PRON
ejpam-3422	101	28	is	be	AUX
ejpam-3422	101	29	a	a	DET
ejpam-3422	101	30	hyper	hyper	ADJ
ejpam-3422	101	31	gr	gr	NOUN
ejpam-3422	101	32	-	-	PUNCT
ejpam-3422	101	33	ideal	ideal	NOUN
ejpam-3422	101	34	of	of	ADP
ejpam-3422	101	35	h	h	NOUN
ejpam-3422	101	36	,	,	PUNCT
ejpam-3422	101	37	a	a	DET
ejpam-3422	101	38	∈	∈	PROPN
ejpam-3422	101	39	i.	i.	NOUN
ejpam-3422	101	40	hence	hence	ADV
ejpam-3422	101	41	,	,	PUNCT
ejpam-3422	101	42	a	a	DET
ejpam-3422	101	43	⊆	⊆	NUM
ejpam-3422	101	44	i.	i.	NOUN
ejpam-3422	101	45	example	example	NOUN
ejpam-3422	101	46	3.9	3.9	NUM
ejpam-3422	101	47	.	.	PUNCT
ejpam-3422	102	1	consider	consider	VERB
ejpam-3422	102	2	a	a	DET
ejpam-3422	102	3	set	set	NOUN
ejpam-3422	102	4	h	h	NOUN
ejpam-3422	102	5	=	=	SYM
ejpam-3422	102	6	{	{	PUNCT
ejpam-3422	102	7	0	0	NUM
ejpam-3422	102	8	,	,	PUNCT
ejpam-3422	102	9	1	1	NUM
ejpam-3422	102	10	,	,	PUNCT
ejpam-3422	102	11	2	2	NUM
ejpam-3422	102	12	}	}	PUNCT
ejpam-3422	102	13	with	with	ADP
ejpam-3422	102	14	the	the	DET
ejpam-3422	102	15	cayley	cayley	ADJ
ejpam-3422	102	16	table	table	NOUN
ejpam-3422	102	17	below	below	ADV
ejpam-3422	102	18	.	.	PUNCT
ejpam-3422	103	1	~	~	PUNCT
ejpam-3422	103	2	0	0	NUM
ejpam-3422	104	1	1	1	NUM
ejpam-3422	104	2	2	2	NUM
ejpam-3422	104	3	0	0	NUM
ejpam-3422	104	4	{	{	PUNCT
ejpam-3422	104	5	0	0	NUM
ejpam-3422	104	6	}	}	PUNCT
ejpam-3422	104	7	{	{	PUNCT
ejpam-3422	104	8	0	0	NUM
ejpam-3422	104	9	}	}	PUNCT
ejpam-3422	104	10	{	{	PUNCT
ejpam-3422	104	11	0	0	NUM
ejpam-3422	104	12	}	}	SYM
ejpam-3422	104	13	1	1	NUM
ejpam-3422	104	14	{	{	PUNCT
ejpam-3422	104	15	0	0	NUM
ejpam-3422	104	16	,	,	PUNCT
ejpam-3422	104	17	1	1	NUM
ejpam-3422	104	18	}	}	PUNCT
ejpam-3422	104	19	{	{	PUNCT
ejpam-3422	104	20	0	0	NUM
ejpam-3422	104	21	,	,	PUNCT
ejpam-3422	104	22	2	2	NUM
ejpam-3422	104	23	}	}	PUNCT
ejpam-3422	104	24	{	{	PUNCT
ejpam-3422	104	25	0	0	NUM
ejpam-3422	104	26	}	}	SYM
ejpam-3422	104	27	2	2	NUM
ejpam-3422	104	28	{	{	PUNCT
ejpam-3422	104	29	0	0	NUM
ejpam-3422	104	30	,	,	PUNCT
ejpam-3422	104	31	2	2	NUM
ejpam-3422	104	32	}	}	PUNCT
ejpam-3422	104	33	{	{	PUNCT
ejpam-3422	104	34	2	2	NUM
ejpam-3422	104	35	}	}	PUNCT
ejpam-3422	104	36	{	{	PUNCT
ejpam-3422	104	37	0	0	NUM
ejpam-3422	104	38	}	}	PUNCT
ejpam-3422	104	39	it	it	PRON
ejpam-3422	104	40	can	can	AUX
ejpam-3422	104	41	be	be	AUX
ejpam-3422	104	42	verified	verify	VERB
ejpam-3422	104	43	that	that	SCONJ
ejpam-3422	104	44	h	h	NOUN
ejpam-3422	104	45	is	be	AUX
ejpam-3422	104	46	a	a	DET
ejpam-3422	104	47	hyper	hyper	ADJ
ejpam-3422	104	48	gr	gr	NOUN
ejpam-3422	104	49	-	-	PUNCT
ejpam-3422	104	50	algebra	algebra	NOUN
ejpam-3422	104	51	and	and	CCONJ
ejpam-3422	104	52	{	{	PUNCT
ejpam-3422	104	53	0	0	NUM
ejpam-3422	104	54	}	}	PUNCT
ejpam-3422	104	55	is	be	AUX
ejpam-3422	104	56	a	a	DET
ejpam-3422	104	57	hyper	hyper	ADJ
ejpam-3422	104	58	gr	gr	NOUN
ejpam-3422	104	59	-	-	PUNCT
ejpam-3422	104	60	ideal	ideal	NOUN
ejpam-3422	104	61	of	of	ADP
ejpam-3422	104	62	h.	h.	PROPN
ejpam-3422	104	63	note	note	VERB
ejpam-3422	104	64	that	that	SCONJ
ejpam-3422	104	65	1~	1~	NUM
ejpam-3422	104	66	(	(	PUNCT
ejpam-3422	104	67	2~	2~	NUM
ejpam-3422	104	68	1	1	NUM
ejpam-3422	104	69	)	)	PUNCT
ejpam-3422	104	70	=	=	PRON
ejpam-3422	104	71	{	{	PUNCT
ejpam-3422	104	72	0	0	NUM
ejpam-3422	104	73	}	}	PUNCT
ejpam-3422	104	74	and	and	CCONJ
ejpam-3422	104	75	1	1	NUM
ejpam-3422	104	76	/∈	/∈	PUNCT
ejpam-3422	104	77	{	{	PUNCT
ejpam-3422	104	78	0	0	NUM
ejpam-3422	104	79	}	}	PUNCT
ejpam-3422	104	80	.	.	PUNCT
ejpam-3422	105	1	since	since	SCONJ
ejpam-3422	105	2	(	(	PUNCT
ejpam-3422	105	3	1~	1~	NUM
ejpam-3422	105	4	0)~	0)~	NOUN
ejpam-3422	105	5	(	(	PUNCT
ejpam-3422	105	6	2~	2~	NUM
ejpam-3422	105	7	1	1	NUM
ejpam-3422	105	8	)	)	PUNCT
ejpam-3422	105	9	=	=	PRON
ejpam-3422	105	10	{	{	PUNCT
ejpam-3422	105	11	0	0	NUM
ejpam-3422	105	12	}	}	PUNCT
ejpam-3422	105	13	and	and	CCONJ
ejpam-3422	105	14	0	0	NUM
ejpam-3422	105	15	∈	∈	NOUN
ejpam-3422	105	16	{	{	PUNCT
ejpam-3422	105	17	0	0	NUM
ejpam-3422	105	18	}	}	PUNCT
ejpam-3422	105	19	but	but	CCONJ
ejpam-3422	105	20	1	1	NUM
ejpam-3422	105	21	/∈	/∈	PUNCT
ejpam-3422	105	22	{	{	PUNCT
ejpam-3422	105	23	0	0	NUM
ejpam-3422	105	24	}	}	PUNCT
ejpam-3422	105	25	,	,	PUNCT
ejpam-3422	105	26	{	{	PUNCT
ejpam-3422	105	27	0	0	X
ejpam-3422	105	28	}	}	PUNCT
ejpam-3422	105	29	is	be	AUX
ejpam-3422	105	30	not	not	PART
ejpam-3422	105	31	an	an	DET
ejpam-3422	105	32	implicative	implicative	ADJ
ejpam-3422	105	33	hyper	hyper	ADJ
ejpam-3422	105	34	gr	gr	NOUN
ejpam-3422	105	35	-	-	PUNCT
ejpam-3422	105	36	ideal	ideal	NOUN
ejpam-3422	105	37	of	of	ADP
ejpam-3422	105	38	h.	h.	PROPN
ejpam-3422	105	39	remark	remark	PROPN
ejpam-3422	105	40	3.10	3.10	NUM
ejpam-3422	105	41	.	.	PUNCT
ejpam-3422	105	42	example	example	NOUN
ejpam-3422	105	43	3.9	3.9	NUM
ejpam-3422	105	44	shows	show	VERB
ejpam-3422	105	45	that	that	SCONJ
ejpam-3422	105	46	not	not	PART
ejpam-3422	105	47	all	all	DET
ejpam-3422	105	48	hyper	hyper	ADJ
ejpam-3422	105	49	gr	gr	ADJ
ejpam-3422	105	50	-	-	PUNCT
ejpam-3422	105	51	ideals	ideal	NOUN
ejpam-3422	105	52	are	be	AUX
ejpam-3422	105	53	implicative	implicative	ADJ
ejpam-3422	105	54	hyper	hyper	ADJ
ejpam-3422	105	55	gr	gr	NOUN
ejpam-3422	105	56	-	-	PUNCT
ejpam-3422	105	57	ideals	ideal	NOUN
ejpam-3422	105	58	.	.	PUNCT
ejpam-3422	106	1	example	example	NOUN
ejpam-3422	106	2	3.11	3.11	NUM
ejpam-3422	106	3	.	.	PUNCT
ejpam-3422	107	1	consider	consider	VERB
ejpam-3422	107	2	the	the	DET
ejpam-3422	107	3	hyper	hyper	ADJ
ejpam-3422	107	4	gr	gr	NOUN
ejpam-3422	107	5	-	-	PUNCT
ejpam-3422	107	6	algebra	algebra	NOUN
ejpam-3422	107	7	h	h	NOUN
ejpam-3422	107	8	in	in	ADP
ejpam-3422	107	9	example	example	NOUN
ejpam-3422	107	10	2.2	2.2	NUM
ejpam-3422	107	11	.	.	PUNCT
ejpam-3422	108	1	by	by	ADP
ejpam-3422	108	2	routine	routine	ADJ
ejpam-3422	108	3	calculations	calculation	NOUN
ejpam-3422	108	4	,	,	PUNCT
ejpam-3422	108	5	it	it	PRON
ejpam-3422	108	6	can	can	AUX
ejpam-3422	108	7	be	be	AUX
ejpam-3422	108	8	shown	show	VERB
ejpam-3422	108	9	that	that	SCONJ
ejpam-3422	108	10	the	the	DET
ejpam-3422	108	11	following	follow	VERB
ejpam-3422	108	12	are	be	AUX
ejpam-3422	108	13	true	true	ADJ
ejpam-3422	108	14	:	:	PUNCT
ejpam-3422	108	15	•	•	NUM
ejpam-3422	108	16	{	{	PUNCT
ejpam-3422	108	17	0	0	NUM
ejpam-3422	108	18	,	,	PUNCT
ejpam-3422	108	19	1	1	NUM
ejpam-3422	108	20	,	,	PUNCT
ejpam-3422	108	21	2	2	NUM
ejpam-3422	108	22	}	}	PUNCT
ejpam-3422	108	23	is	be	AUX
ejpam-3422	108	24	a	a	DET
ejpam-3422	108	25	hyper	hyper	ADJ
ejpam-3422	108	26	gr	gr	NOUN
ejpam-3422	108	27	-	-	PUNCT
ejpam-3422	108	28	ideal	ideal	NOUN
ejpam-3422	108	29	of	of	ADP
ejpam-3422	108	30	h.	h.	PROPN
ejpam-3422	108	31	•	•	PROPN
ejpam-3422	108	32	for	for	ADP
ejpam-3422	108	33	any	any	DET
ejpam-3422	108	34	x	x	NOUN
ejpam-3422	108	35	,	,	PUNCT
ejpam-3422	108	36	y,∈	y,∈	NUM
ejpam-3422	108	37	h	h	NOUN
ejpam-3422	108	38	such	such	ADJ
ejpam-3422	108	39	that	that	SCONJ
ejpam-3422	108	40	x~	x~	PROPN
ejpam-3422	108	41	(	(	PUNCT
ejpam-3422	108	42	y	y	NOUN
ejpam-3422	108	43	~	~	PUNCT
ejpam-3422	108	44	x	x	X
ejpam-3422	108	45	)	)	PUNCT
ejpam-3422	108	46	⊆	⊆	NUM
ejpam-3422	108	47	{	{	PUNCT
ejpam-3422	108	48	0	0	NUM
ejpam-3422	108	49	,	,	PUNCT
ejpam-3422	108	50	1	1	NUM
ejpam-3422	108	51	,	,	PUNCT
ejpam-3422	108	52	2	2	NUM
ejpam-3422	108	53	}	}	PUNCT
ejpam-3422	108	54	implies	imply	VERB
ejpam-3422	108	55	that	that	SCONJ
ejpam-3422	108	56	x	x	SYM
ejpam-3422	108	57	∈	∈	PROPN
ejpam-3422	108	58	{	{	PUNCT
ejpam-3422	108	59	0	0	NUM
ejpam-3422	108	60	,	,	PUNCT
ejpam-3422	108	61	1	1	NUM
ejpam-3422	108	62	,	,	PUNCT
ejpam-3422	108	63	2	2	NUM
ejpam-3422	108	64	}	}	PUNCT
ejpam-3422	108	65	.	.	PUNCT
ejpam-3422	109	1	moreover	moreover	ADV
ejpam-3422	109	2	,	,	PUNCT
ejpam-3422	109	3	{	{	PUNCT
ejpam-3422	109	4	0	0	NUM
ejpam-3422	109	5	,	,	PUNCT
ejpam-3422	109	6	1	1	NUM
ejpam-3422	109	7	,	,	PUNCT
ejpam-3422	109	8	2	2	NUM
ejpam-3422	109	9	}	}	PUNCT
ejpam-3422	109	10	can	can	AUX
ejpam-3422	109	11	be	be	AUX
ejpam-3422	109	12	verified	verify	VERB
ejpam-3422	109	13	to	to	PART
ejpam-3422	109	14	be	be	AUX
ejpam-3422	109	15	an	an	DET
ejpam-3422	109	16	implicative	implicative	ADJ
ejpam-3422	109	17	hyper	hyper	ADJ
ejpam-3422	109	18	gr	gr	NOUN
ejpam-3422	109	19	-	-	PUNCT
ejpam-3422	109	20	ideal	ideal	NOUN
ejpam-3422	109	21	of	of	ADP
ejpam-3422	109	22	h.	h.	PROPN
ejpam-3422	109	23	the	the	DET
ejpam-3422	109	24	preceding	precede	VERB
ejpam-3422	109	25	example	example	NOUN
ejpam-3422	109	26	is	be	AUX
ejpam-3422	109	27	generalized	generalize	VERB
ejpam-3422	109	28	in	in	ADP
ejpam-3422	109	29	the	the	DET
ejpam-3422	109	30	following	follow	VERB
ejpam-3422	109	31	proposition	proposition	NOUN
ejpam-3422	109	32	.	.	PUNCT
ejpam-3422	110	1	proposition	proposition	NOUN
ejpam-3422	110	2	3.12	3.12	NUM
ejpam-3422	110	3	.	.	PUNCT
ejpam-3422	111	1	let	let	VERB
ejpam-3422	111	2	i	i	PRON
ejpam-3422	111	3	be	be	AUX
ejpam-3422	111	4	a	a	DET
ejpam-3422	111	5	hyper	hyper	ADJ
ejpam-3422	111	6	gr	gr	NOUN
ejpam-3422	111	7	-	-	PUNCT
ejpam-3422	111	8	ideal	ideal	NOUN
ejpam-3422	111	9	of	of	ADP
ejpam-3422	111	10	h.	h.	NOUN
ejpam-3422	112	1	if	if	SCONJ
ejpam-3422	112	2	x	x	PRON
ejpam-3422	112	3	~	~	PUNCT
ejpam-3422	112	4	(	(	PUNCT
ejpam-3422	112	5	y	y	NOUN
ejpam-3422	112	6	~	~	PUNCT
ejpam-3422	112	7	x	x	X
ejpam-3422	112	8	)	)	PUNCT
ejpam-3422	112	9	⊆	⊆	NUM
ejpam-3422	112	10	i	i	PRON
ejpam-3422	112	11	implies	imply	VERB
ejpam-3422	112	12	x	x	PUNCT
ejpam-3422	112	13	∈	∈	PROPN
ejpam-3422	112	14	i	i	PRON
ejpam-3422	112	15	,	,	PUNCT
ejpam-3422	112	16	then	then	ADV
ejpam-3422	112	17	i	i	PRON
ejpam-3422	112	18	is	be	AUX
ejpam-3422	112	19	implicative	implicative	ADJ
ejpam-3422	112	20	hyper	hyper	ADJ
ejpam-3422	112	21	gr	gr	NOUN
ejpam-3422	112	22	-	-	PUNCT
ejpam-3422	112	23	ideal	ideal	NOUN
ejpam-3422	112	24	of	of	ADP
ejpam-3422	112	25	h.	h.	PROPN
ejpam-3422	112	26	a.	a.	PROPN
ejpam-3422	112	27	macodi	macodi	PROPN
ejpam-3422	112	28	-	-	PUNCT
ejpam-3422	112	29	ringia	ringia	ADJ
ejpam-3422	112	30	,	,	PUNCT
ejpam-3422	112	31	g.	g.	PROPN
ejpam-3422	112	32	petalcorin	petalcorin	PROPN
ejpam-3422	112	33	,	,	PUNCT
ejpam-3422	112	34	jr	jr	PROPN
ejpam-3422	112	35	.	.	PROPN
ejpam-3422	112	36	/	/	SYM
ejpam-3422	112	37	eur	eur	PROPN
ejpam-3422	112	38	.	.	PUNCT
ejpam-3422	113	1	j.	j.	PROPN
ejpam-3422	113	2	pure	pure	PROPN
ejpam-3422	113	3	appl	appl	PROPN
ejpam-3422	113	4	.	.	PROPN
ejpam-3422	113	5	math	math	PROPN
ejpam-3422	113	6	,	,	PUNCT
ejpam-3422	113	7	12	12	NUM
ejpam-3422	113	8	(	(	PUNCT
ejpam-3422	113	9	2	2	NUM
ejpam-3422	113	10	)	)	PUNCT
ejpam-3422	113	11	(	(	PUNCT
ejpam-3422	113	12	2019	2019	NUM
ejpam-3422	113	13	)	)	PUNCT
ejpam-3422	113	14	,	,	PUNCT
ejpam-3422	113	15	409	409	NUM
ejpam-3422	113	16	-	-	SYM
ejpam-3422	113	17	417	417	NUM
ejpam-3422	113	18	414	414	NUM
ejpam-3422	113	19	proof	proof	NOUN
ejpam-3422	113	20	.	.	PUNCT
ejpam-3422	114	1	let	let	VERB
ejpam-3422	114	2	x	x	PRON
ejpam-3422	114	3	,	,	PUNCT
ejpam-3422	114	4	y	y	PROPN
ejpam-3422	114	5	,	,	PUNCT
ejpam-3422	114	6	z	z	PROPN
ejpam-3422	114	7	∈	∈	PROPN
ejpam-3422	114	8	h	h	NOUN
ejpam-3422	114	9	such	such	ADJ
ejpam-3422	114	10	that	that	SCONJ
ejpam-3422	114	11	(	(	PUNCT
ejpam-3422	114	12	x	x	X
ejpam-3422	114	13	~	~	PUNCT
ejpam-3422	114	14	z	z	X
ejpam-3422	114	15	)	)	PUNCT
ejpam-3422	114	16	~	~	PUNCT
ejpam-3422	114	17	(	(	PUNCT
ejpam-3422	114	18	y	y	X
ejpam-3422	114	19	~	~	PUNCT
ejpam-3422	114	20	x	x	X
ejpam-3422	114	21	)	)	PUNCT
ejpam-3422	115	1	⊆	⊆	NUM
ejpam-3422	115	2	i	i	PROPN
ejpam-3422	115	3	and	and	CCONJ
ejpam-3422	115	4	z	z	PROPN
ejpam-3422	115	5	∈	∈	PROPN
ejpam-3422	115	6	i.	i.	NOUN
ejpam-3422	115	7	by	by	ADP
ejpam-3422	115	8	hgr2	hgr2	NOUN
ejpam-3422	115	9	,	,	PUNCT
ejpam-3422	115	10	[	[	X
ejpam-3422	115	11	x	x	X
ejpam-3422	115	12	~	~	PUNCT
ejpam-3422	115	13	(	(	PUNCT
ejpam-3422	115	14	y	y	X
ejpam-3422	115	15	~	~	PUNCT
ejpam-3422	115	16	x	x	X
ejpam-3422	115	17	)	)	PUNCT
ejpam-3422	115	18	]	]	PUNCT
ejpam-3422	116	1	~	~	PUNCT
ejpam-3422	116	2	z	z	X
ejpam-3422	116	3	=	=	SYM
ejpam-3422	116	4	(	(	PUNCT
ejpam-3422	116	5	x	x	SYM
ejpam-3422	116	6	~	~	PUNCT
ejpam-3422	116	7	z	z	X
ejpam-3422	116	8	)	)	PUNCT
ejpam-3422	116	9	~	~	PUNCT
ejpam-3422	116	10	(	(	PUNCT
ejpam-3422	116	11	y	y	X
ejpam-3422	116	12	~	~	PUNCT
ejpam-3422	116	13	x	x	X
ejpam-3422	116	14	)	)	PUNCT
ejpam-3422	116	15	⊆	⊆	NUM
ejpam-3422	116	16	i.	i.	NOUN
ejpam-3422	116	17	by	by	ADP
ejpam-3422	116	18	lemma	lemma	PROPN
ejpam-3422	116	19	3.8	3.8	NUM
ejpam-3422	116	20	,	,	PUNCT
ejpam-3422	116	21	x	x	X
ejpam-3422	116	22	~	~	PUNCT
ejpam-3422	116	23	(	(	PUNCT
ejpam-3422	116	24	y	y	NOUN
ejpam-3422	116	25	~	~	PUNCT
ejpam-3422	116	26	x	x	X
ejpam-3422	116	27	)	)	PUNCT
ejpam-3422	116	28	⊆	⊆	NUM
ejpam-3422	116	29	i.	i.	NOUN
ejpam-3422	116	30	thus	thus	ADV
ejpam-3422	116	31	,	,	PUNCT
ejpam-3422	116	32	x	x	PUNCT
ejpam-3422	116	33	∈	∈	PROPN
ejpam-3422	116	34	i	i	PRON
ejpam-3422	116	35	and	and	CCONJ
ejpam-3422	116	36	so	so	ADV
ejpam-3422	116	37	i	i	PRON
ejpam-3422	116	38	is	be	AUX
ejpam-3422	116	39	implicative	implicative	ADJ
ejpam-3422	116	40	hyper	hyper	ADJ
ejpam-3422	116	41	gr	gr	NOUN
ejpam-3422	116	42	-	-	PUNCT
ejpam-3422	116	43	ideal	ideal	NOUN
ejpam-3422	116	44	of	of	ADP
ejpam-3422	116	45	h.	h.	PROPN
ejpam-3422	116	46	the	the	DET
ejpam-3422	116	47	converse	converse	NOUN
ejpam-3422	116	48	of	of	ADP
ejpam-3422	116	49	proposition	proposition	NOUN
ejpam-3422	116	50	3.12	3.12	NUM
ejpam-3422	116	51	does	do	AUX
ejpam-3422	116	52	not	not	PART
ejpam-3422	116	53	hold	hold	VERB
ejpam-3422	116	54	in	in	ADP
ejpam-3422	116	55	general	general	ADJ
ejpam-3422	116	56	as	as	SCONJ
ejpam-3422	116	57	shown	show	VERB
ejpam-3422	116	58	in	in	ADP
ejpam-3422	116	59	the	the	DET
ejpam-3422	116	60	following	follow	VERB
ejpam-3422	116	61	example	example	NOUN
ejpam-3422	116	62	.	.	PUNCT
ejpam-3422	116	63	example	example	NOUN
ejpam-3422	116	64	3.13	3.13	NUM
ejpam-3422	116	65	.	.	PUNCT
ejpam-3422	117	1	consider	consider	VERB
ejpam-3422	117	2	the	the	DET
ejpam-3422	117	3	hyper	hyper	ADJ
ejpam-3422	117	4	gr	gr	NOUN
ejpam-3422	117	5	-	-	PUNCT
ejpam-3422	117	6	algebra	algebra	NOUN
ejpam-3422	117	7	h	h	NOUN
ejpam-3422	117	8	in	in	ADP
ejpam-3422	117	9	example	example	NOUN
ejpam-3422	117	10	3.2	3.2	NUM
ejpam-3422	117	11	.	.	PUNCT
ejpam-3422	118	1	i	i	PRON
ejpam-3422	118	2	=	=	PUNCT
ejpam-3422	118	3	{	{	PUNCT
ejpam-3422	118	4	0	0	NUM
ejpam-3422	118	5	,	,	PUNCT
ejpam-3422	118	6	1	1	NUM
ejpam-3422	118	7	,	,	PUNCT
ejpam-3422	118	8	2	2	NUM
ejpam-3422	118	9	}	}	PUNCT
ejpam-3422	118	10	can	can	AUX
ejpam-3422	118	11	be	be	AUX
ejpam-3422	118	12	verified	verify	VERB
ejpam-3422	118	13	to	to	PART
ejpam-3422	118	14	be	be	AUX
ejpam-3422	118	15	both	both	PRON
ejpam-3422	118	16	hyper	hyper	ADJ
ejpam-3422	118	17	gr	gr	ADJ
ejpam-3422	118	18	-	-	PUNCT
ejpam-3422	118	19	ideal	ideal	ADJ
ejpam-3422	118	20	and	and	CCONJ
ejpam-3422	118	21	implicative	implicative	ADJ
ejpam-3422	118	22	hyper	hyper	ADJ
ejpam-3422	118	23	gr	gr	NOUN
ejpam-3422	118	24	-	-	PUNCT
ejpam-3422	118	25	ideal	ideal	NOUN
ejpam-3422	118	26	of	of	ADP
ejpam-3422	118	27	h.	h.	PROPN
ejpam-3422	118	28	but	but	CCONJ
ejpam-3422	118	29	3~(2~3	3~(2~3	NUM
ejpam-3422	118	30	)	)	PUNCT
ejpam-3422	118	31	=	=	PRON
ejpam-3422	118	32	{	{	PUNCT
ejpam-3422	118	33	0	0	NUM
ejpam-3422	118	34	}	}	PUNCT
ejpam-3422	118	35	⊆	⊆	NUM
ejpam-3422	118	36	{	{	PUNCT
ejpam-3422	118	37	0	0	NUM
ejpam-3422	118	38	,	,	PUNCT
ejpam-3422	118	39	1	1	NUM
ejpam-3422	118	40	,	,	PUNCT
ejpam-3422	118	41	2	2	NUM
ejpam-3422	118	42	}	}	PUNCT
ejpam-3422	118	43	and	and	CCONJ
ejpam-3422	118	44	3	3	NUM
ejpam-3422	118	45	/∈	/∈	PUNCT
ejpam-3422	118	46	{	{	PUNCT
ejpam-3422	118	47	0	0	NUM
ejpam-3422	118	48	,	,	PUNCT
ejpam-3422	118	49	1	1	NUM
ejpam-3422	118	50	,	,	PUNCT
ejpam-3422	118	51	2	2	NUM
ejpam-3422	118	52	}	}	PUNCT
ejpam-3422	118	53	=	=	SYM
ejpam-3422	118	54	i.	i.	NOUN
ejpam-3422	118	55	proposition	proposition	NOUN
ejpam-3422	118	56	3.14	3.14	NUM
ejpam-3422	118	57	.	.	PUNCT
ejpam-3422	119	1	let	let	VERB
ejpam-3422	119	2	i	i	PRON
ejpam-3422	119	3	be	be	AUX
ejpam-3422	119	4	a	a	DET
ejpam-3422	119	5	hyper	hyper	ADJ
ejpam-3422	119	6	subgr	subgr	NOUN
ejpam-3422	119	7	-	-	PUNCT
ejpam-3422	119	8	algebra	algebra	NOUN
ejpam-3422	119	9	of	of	ADP
ejpam-3422	119	10	a	a	DET
ejpam-3422	119	11	hyper	hyper	ADJ
ejpam-3422	119	12	gr	gr	NOUN
ejpam-3422	119	13	-	-	PUNCT
ejpam-3422	119	14	algebra	algebra	NOUN
ejpam-3422	119	15	h.	h.	NOUN
ejpam-3422	119	16	if	if	SCONJ
ejpam-3422	119	17	i	i	PRON
ejpam-3422	119	18	is	be	AUX
ejpam-3422	119	19	an	an	DET
ejpam-3422	119	20	implicative	implicative	ADJ
ejpam-3422	119	21	hyper	hyper	ADJ
ejpam-3422	119	22	gr	gr	NOUN
ejpam-3422	119	23	-	-	PUNCT
ejpam-3422	119	24	ideal	ideal	NOUN
ejpam-3422	119	25	,	,	PUNCT
ejpam-3422	119	26	then	then	ADV
ejpam-3422	119	27	x~	x~	PROPN
ejpam-3422	119	28	(	(	PUNCT
ejpam-3422	119	29	y	y	NOUN
ejpam-3422	119	30	~	~	PUNCT
ejpam-3422	119	31	x	x	X
ejpam-3422	119	32	)	)	PUNCT
ejpam-3422	119	33	⊆	⊆	NUM
ejpam-3422	119	34	i	i	PRON
ejpam-3422	119	35	implies	imply	VERB
ejpam-3422	119	36	x	x	PUNCT
ejpam-3422	119	37	∈	∈	NOUN
ejpam-3422	119	38	i.	i.	NOUN
ejpam-3422	119	39	proof	proof	NOUN
ejpam-3422	119	40	.	.	PUNCT
ejpam-3422	120	1	let	let	VERB
ejpam-3422	120	2	x	x	PRON
ejpam-3422	120	3	,	,	PUNCT
ejpam-3422	120	4	y	y	PROPN
ejpam-3422	120	5	,	,	PUNCT
ejpam-3422	120	6	z	z	PROPN
ejpam-3422	120	7	∈	∈	PROPN
ejpam-3422	120	8	h	h	NOUN
ejpam-3422	120	9	such	such	ADJ
ejpam-3422	120	10	that	that	SCONJ
ejpam-3422	120	11	x~	x~	PROPN
ejpam-3422	120	12	(	(	PUNCT
ejpam-3422	120	13	y	y	PROPN
ejpam-3422	120	14	~	~	SYM
ejpam-3422	120	15	x	x	X
ejpam-3422	120	16	)	)	PUNCT
ejpam-3422	120	17	⊆	⊆	NUM
ejpam-3422	120	18	i	i	PRON
ejpam-3422	120	19	and	and	CCONJ
ejpam-3422	120	20	let	let	VERB
ejpam-3422	120	21	z	z	PROPN
ejpam-3422	120	22	∈	∈	PROPN
ejpam-3422	120	23	i.	i.	NOUN
ejpam-3422	120	24	it	it	PRON
ejpam-3422	120	25	follows	follow	VERB
ejpam-3422	120	26	from	from	ADP
ejpam-3422	120	27	theorem	theorem	ADJ
ejpam-3422	120	28	2.4	2.4	NUM
ejpam-3422	120	29	,	,	PUNCT
ejpam-3422	120	30	[	[	X
ejpam-3422	120	31	x~	x~	PROPN
ejpam-3422	120	32	(	(	PUNCT
ejpam-3422	120	33	y	y	NOUN
ejpam-3422	120	34	~	~	PUNCT
ejpam-3422	120	35	x	x	X
ejpam-3422	120	36	)	)	PUNCT
ejpam-3422	120	37	]	]	PUNCT
ejpam-3422	121	1	~	~	PUNCT
ejpam-3422	121	2	z	z	X
ejpam-3422	121	3	∈	∈	PROPN
ejpam-3422	121	4	i.	i.	NOUN
ejpam-3422	121	5	by	by	ADP
ejpam-3422	121	6	hgr2	hgr2	NOUN
ejpam-3422	121	7	,	,	PUNCT
ejpam-3422	121	8	(	(	PUNCT
ejpam-3422	121	9	x~	x~	PROPN
ejpam-3422	121	10	z	z	PROPN
ejpam-3422	121	11	)	)	PUNCT
ejpam-3422	121	12	~	~	PUNCT
ejpam-3422	121	13	(	(	PUNCT
ejpam-3422	121	14	y	y	X
ejpam-3422	121	15	~	~	PUNCT
ejpam-3422	121	16	x	x	X
ejpam-3422	121	17	)	)	PUNCT
ejpam-3422	121	18	=	=	NOUN
ejpam-3422	122	1	[	[	X
ejpam-3422	122	2	x~	x~	PROPN
ejpam-3422	122	3	(	(	PUNCT
ejpam-3422	122	4	y	y	NOUN
ejpam-3422	122	5	~	~	PUNCT
ejpam-3422	122	6	x	x	X
ejpam-3422	122	7	)	)	PUNCT
ejpam-3422	122	8	]	]	PUNCT
ejpam-3422	122	9	⊆	⊆	NUM
ejpam-3422	122	10	i.	i.	NOUN
ejpam-3422	122	11	since	since	SCONJ
ejpam-3422	122	12	i	i	PRON
ejpam-3422	122	13	is	be	AUX
ejpam-3422	122	14	an	an	DET
ejpam-3422	122	15	implicative	implicative	ADJ
ejpam-3422	122	16	hyper	hyper	ADJ
ejpam-3422	122	17	gr	gr	NOUN
ejpam-3422	122	18	-	-	PUNCT
ejpam-3422	122	19	ideals	ideal	NOUN
ejpam-3422	122	20	,	,	PUNCT
ejpam-3422	122	21	x	x	SYM
ejpam-3422	122	22	∈	∈	PROPN
ejpam-3422	122	23	i.	i.	NOUN
ejpam-3422	122	24	proposition	proposition	NOUN
ejpam-3422	122	25	3.15	3.15	NUM
ejpam-3422	122	26	.	.	PUNCT
ejpam-3422	123	1	let	let	VERB
ejpam-3422	123	2	a	a	DET
ejpam-3422	123	3	,	,	PUNCT
ejpam-3422	123	4	b	b	NOUN
ejpam-3422	123	5	and	and	CCONJ
ejpam-3422	123	6	c	c	PROPN
ejpam-3422	123	7	be	be	AUX
ejpam-3422	123	8	subsets	subset	NOUN
ejpam-3422	123	9	of	of	ADP
ejpam-3422	123	10	a	a	DET
ejpam-3422	123	11	hyper	hyper	ADJ
ejpam-3422	123	12	gr	gr	NOUN
ejpam-3422	123	13	-	-	PUNCT
ejpam-3422	123	14	algebra	algebra	NOUN
ejpam-3422	123	15	h.	h.	NOUN
ejpam-3422	123	16	if	if	SCONJ
ejpam-3422	123	17	i	i	PRON
ejpam-3422	123	18	is	be	AUX
ejpam-3422	123	19	implicative	implicative	ADJ
ejpam-3422	123	20	hyper	hyper	ADJ
ejpam-3422	123	21	gr	gr	NOUN
ejpam-3422	123	22	-	-	PUNCT
ejpam-3422	123	23	ideal	ideal	NOUN
ejpam-3422	123	24	of	of	ADP
ejpam-3422	123	25	h	h	NOUN
ejpam-3422	123	26	,	,	PUNCT
ejpam-3422	123	27	then	then	ADV
ejpam-3422	123	28	(	(	PUNCT
ejpam-3422	123	29	a~	a~	PROPN
ejpam-3422	123	30	c	c	PROPN
ejpam-3422	123	31	)	)	PUNCT
ejpam-3422	123	32	~	~	PUNCT
ejpam-3422	124	1	(	(	PUNCT
ejpam-3422	124	2	b	b	X
ejpam-3422	124	3	~a	~a	NOUN
ejpam-3422	124	4	)	)	PUNCT
ejpam-3422	124	5	⊆	⊆	NUM
ejpam-3422	124	6	i	i	PROPN
ejpam-3422	124	7	and	and	CCONJ
ejpam-3422	124	8	c	c	NOUN
ejpam-3422	124	9	⊆	⊆	NUM
ejpam-3422	124	10	i	i	PRON
ejpam-3422	124	11	imply	imply	VERB
ejpam-3422	124	12	a	a	DET
ejpam-3422	124	13	⊆	⊆	NUM
ejpam-3422	124	14	i.	i.	NOUN
ejpam-3422	124	15	proof	proof	NOUN
ejpam-3422	124	16	.	.	PUNCT
ejpam-3422	125	1	suppose	suppose	VERB
ejpam-3422	125	2	(	(	PUNCT
ejpam-3422	125	3	a	a	DET
ejpam-3422	125	4	~	~	PROPN
ejpam-3422	125	5	c)~(b	c)~(b	X
ejpam-3422	125	6	~	~	SYM
ejpam-3422	125	7	a	a	X
ejpam-3422	125	8	)	)	PUNCT
ejpam-3422	125	9	⊆	⊆	NUM
ejpam-3422	125	10	i	i	PROPN
ejpam-3422	125	11	and	and	CCONJ
ejpam-3422	125	12	c	c	PROPN
ejpam-3422	125	13	⊆	⊆	NUM
ejpam-3422	125	14	i.	i.	NOUN
ejpam-3422	125	15	let	let	VERB
ejpam-3422	125	16	a	a	DET
ejpam-3422	125	17	∈	∈	NOUN
ejpam-3422	125	18	a.	a.	NOUN
ejpam-3422	125	19	then	then	ADV
ejpam-3422	125	20	,	,	PUNCT
ejpam-3422	125	21	(	(	PUNCT
ejpam-3422	125	22	a	a	PRON
ejpam-3422	125	23	~	~	PROPN
ejpam-3422	125	24	c)~(b	c)~(b	X
ejpam-3422	125	25	~	~	SYM
ejpam-3422	125	26	a	a	X
ejpam-3422	125	27	)	)	PUNCT
ejpam-3422	125	28	⊆	⊆	NUM
ejpam-3422	125	29	i	i	PRON
ejpam-3422	125	30	for	for	ADP
ejpam-3422	125	31	c	c	PROPN
ejpam-3422	125	32	∈	∈	PROPN
ejpam-3422	125	33	c	c	NOUN
ejpam-3422	125	34	⊆	⊆	NUM
ejpam-3422	125	35	i	i	PROPN
ejpam-3422	125	36	and	and	CCONJ
ejpam-3422	125	37	b	b	PROPN
ejpam-3422	125	38	∈	∈	PROPN
ejpam-3422	125	39	b.	b.	PROPN
ejpam-3422	125	40	since	since	SCONJ
ejpam-3422	125	41	i	i	PRON
ejpam-3422	125	42	is	be	AUX
ejpam-3422	125	43	implicative	implicative	ADJ
ejpam-3422	125	44	hyper	hyper	ADJ
ejpam-3422	125	45	gr	gr	NOUN
ejpam-3422	125	46	-	-	PUNCT
ejpam-3422	125	47	ideal	ideal	NOUN
ejpam-3422	125	48	of	of	ADP
ejpam-3422	125	49	h	h	NOUN
ejpam-3422	125	50	,	,	PUNCT
ejpam-3422	125	51	x	x	SYM
ejpam-3422	125	52	∈	∈	PROPN
ejpam-3422	125	53	i.	i.	NOUN
ejpam-3422	125	54	hence	hence	ADV
ejpam-3422	125	55	,	,	PUNCT
ejpam-3422	125	56	a	a	DET
ejpam-3422	125	57	⊆	⊆	NUM
ejpam-3422	125	58	i.	i.	NOUN
ejpam-3422	125	59	4	4	NUM
ejpam-3422	125	60	.	.	PUNCT
ejpam-3422	125	61	fuzzy	fuzzy	ADJ
ejpam-3422	125	62	implicative	implicative	ADJ
ejpam-3422	125	63	hyper	hyper	ADJ
ejpam-3422	125	64	gr	gr	ADJ
ejpam-3422	125	65	-	-	PUNCT
ejpam-3422	125	66	ideals	ideal	NOUN
ejpam-3422	125	67	definition	definition	NOUN
ejpam-3422	125	68	4.1	4.1	NUM
ejpam-3422	125	69	.	.	PUNCT
ejpam-3422	126	1	a	a	DET
ejpam-3422	126	2	fuzzy	fuzzy	ADJ
ejpam-3422	126	3	set	set	VERB
ejpam-3422	126	4	µ	µ	NOUN
ejpam-3422	126	5	in	in	ADP
ejpam-3422	126	6	a	a	DET
ejpam-3422	126	7	hyper	hyper	ADJ
ejpam-3422	126	8	gr	gr	NOUN
ejpam-3422	126	9	-	-	PUNCT
ejpam-3422	126	10	algebra	algebra	NOUN
ejpam-3422	126	11	h	h	NOUN
ejpam-3422	126	12	is	be	AUX
ejpam-3422	126	13	called	call	VERB
ejpam-3422	126	14	a	a	DET
ejpam-3422	126	15	fuzzy	fuzzy	ADJ
ejpam-3422	126	16	implicative	implicative	ADJ
ejpam-3422	126	17	hyper	hyper	ADJ
ejpam-3422	126	18	gr	gr	NOUN
ejpam-3422	126	19	-	-	PUNCT
ejpam-3422	126	20	ideal	ideal	NOUN
ejpam-3422	126	21	of	of	ADP
ejpam-3422	126	22	type	type	NOUN
ejpam-3422	126	23	1	1	NUM
ejpam-3422	126	24	in	in	ADP
ejpam-3422	126	25	h	h	NOUN
ejpam-3422	126	26	if	if	SCONJ
ejpam-3422	126	27	(	(	PUNCT
ejpam-3422	126	28	fim1	fim1	PROPN
ejpam-3422	126	29	)	)	PUNCT
ejpam-3422	126	30	µ(0	µ(0	NOUN
ejpam-3422	126	31	)	)	PUNCT
ejpam-3422	126	32	≥	≥	NOUN
ejpam-3422	126	33	µ(x	µ(x	NOUN
ejpam-3422	126	34	)	)	PUNCT
ejpam-3422	126	35	≥	≥	NOUN
ejpam-3422	126	36	min	min	PROPN
ejpam-3422	126	37	{	{	PUNCT
ejpam-3422	126	38	inf	inf	NOUN
ejpam-3422	126	39	u∈(x	u∈(x	PROPN
ejpam-3422	126	40	~	~	SYM
ejpam-3422	126	41	z)~(y	z)~(y	PROPN
ejpam-3422	126	42	~	~	SYM
ejpam-3422	126	43	x	x	X
ejpam-3422	126	44	)	)	PUNCT
ejpam-3422	126	45	µ(u	µ(u	NOUN
ejpam-3422	126	46	)	)	PUNCT
ejpam-3422	126	47	,	,	PUNCT
ejpam-3422	126	48	µ(z	µ(z	PROPN
ejpam-3422	126	49	)	)	PUNCT
ejpam-3422	126	50	}	}	PUNCT
ejpam-3422	126	51	for	for	ADP
ejpam-3422	126	52	x	x	PROPN
ejpam-3422	126	53	,	,	PUNCT
ejpam-3422	126	54	y	y	PROPN
ejpam-3422	126	55	,	,	PUNCT
ejpam-3422	126	56	z	z	PROPN
ejpam-3422	126	57	∈	∈	PROPN
ejpam-3422	126	58	h.	h.	PROPN
ejpam-3422	126	59	example	example	NOUN
ejpam-3422	126	60	4.2	4.2	NUM
ejpam-3422	126	61	.	.	PUNCT
ejpam-3422	127	1	consider	consider	VERB
ejpam-3422	127	2	the	the	DET
ejpam-3422	127	3	hyper	hyper	ADJ
ejpam-3422	127	4	gr	gr	NOUN
ejpam-3422	127	5	-	-	PUNCT
ejpam-3422	127	6	algebra	algebra	NOUN
ejpam-3422	127	7	h	h	NOUN
ejpam-3422	128	1	=	=	PUNCT
ejpam-3422	129	1	[	[	X
ejpam-3422	129	2	0	0	NUM
ejpam-3422	129	3	,	,	PUNCT
ejpam-3422	129	4	1	1	NUM
ejpam-3422	129	5	]	]	PUNCT
ejpam-3422	129	6	such	such	ADJ
ejpam-3422	129	7	that	that	PRON
ejpam-3422	129	8	for	for	ADP
ejpam-3422	129	9	any	any	DET
ejpam-3422	129	10	x	x	NOUN
ejpam-3422	129	11	,	,	PUNCT
ejpam-3422	129	12	y	y	PROPN
ejpam-3422	129	13	∈	∈	PROPN
ejpam-3422	130	1	[	[	X
ejpam-3422	130	2	0	0	NUM
ejpam-3422	130	3	,	,	PUNCT
ejpam-3422	130	4	1	1	NUM
ejpam-3422	130	5	]	]	PUNCT
ejpam-3422	130	6	,	,	PUNCT
ejpam-3422	130	7	x~	x~	PROPN
ejpam-3422	130	8	y	y	X
ejpam-3422	130	9	=	=	PUNCT
ejpam-3422	130	10	{	{	PUNCT
ejpam-3422	131	1	[	[	X
ejpam-3422	131	2	0	0	NUM
ejpam-3422	131	3	,	,	PUNCT
ejpam-3422	131	4	0.3	0.3	NUM
ejpam-3422	131	5	]	]	PUNCT
ejpam-3422	131	6	,	,	PUNCT
ejpam-3422	131	7	if	if	SCONJ
ejpam-3422	131	8	y	y	PROPN
ejpam-3422	131	9	6=	6=	ADP
ejpam-3422	131	10	0	0	NUM
ejpam-3422	131	11	or	or	CCONJ
ejpam-3422	131	12	x	x	SYM
ejpam-3422	131	13	=	=	SYM
ejpam-3422	131	14	0	0	NUM
ejpam-3422	131	15	=	=	SYM
ejpam-3422	131	16	y	y	PROPN
ejpam-3422	131	17	,	,	PUNCT
ejpam-3422	131	18	{	{	PUNCT
ejpam-3422	131	19	x	x	X
ejpam-3422	131	20	}	}	PUNCT
ejpam-3422	131	21	,	,	PUNCT
ejpam-3422	131	22	if	if	SCONJ
ejpam-3422	131	23	x	x	PROPN
ejpam-3422	131	24	6=	6=	ADP
ejpam-3422	131	25	0	0	NUM
ejpam-3422	131	26	and	and	CCONJ
ejpam-3422	131	27	y	y	PROPN
ejpam-3422	131	28	=	=	SYM
ejpam-3422	131	29	0	0	X
ejpam-3422	131	30	.	.	PUNCT
ejpam-3422	131	31	define	define	VERB
ejpam-3422	131	32	a	a	DET
ejpam-3422	131	33	fuzzy	fuzzy	ADJ
ejpam-3422	131	34	set	set	VERB
ejpam-3422	131	35	µ	µ	NOUN
ejpam-3422	131	36	in	in	ADP
ejpam-3422	131	37	h	h	NOUN
ejpam-3422	131	38	by	by	ADP
ejpam-3422	131	39	µ(x	µ(x	NOUN
ejpam-3422	131	40	)	)	PUNCT
ejpam-3422	131	41	=	=	PUNCT
ejpam-3422	132	1			PROPN
ejpam-3422	132	2	1	1	NUM
ejpam-3422	132	3	,	,	PUNCT
ejpam-3422	132	4	if	if	SCONJ
ejpam-3422	132	5	x	x	ADP
ejpam-3422	132	6	=	=	SYM
ejpam-3422	132	7	0	0	NUM
ejpam-3422	132	8	,	,	PUNCT
ejpam-3422	132	9	0.3	0.3	NUM
ejpam-3422	133	1	+	+	CCONJ
ejpam-3422	133	2	x	x	X
ejpam-3422	133	3	,	,	PUNCT
ejpam-3422	133	4	if	if	SCONJ
ejpam-3422	133	5	x	x	SYM
ejpam-3422	133	6	∈	∈	PROPN
ejpam-3422	133	7	(	(	PUNCT
ejpam-3422	133	8	0	0	NUM
ejpam-3422	133	9	,	,	PUNCT
ejpam-3422	133	10	0.3	0.3	NUM
ejpam-3422	133	11	]	]	PUNCT
ejpam-3422	133	12	,	,	PUNCT
ejpam-3422	133	13	0.7	0.7	NUM
ejpam-3422	133	14	,	,	PUNCT
ejpam-3422	133	15	if	if	SCONJ
ejpam-3422	133	16	x	x	SYM
ejpam-3422	133	17	∈	∈	PROPN
ejpam-3422	133	18	(	(	PUNCT
ejpam-3422	133	19	0.3	0.3	NUM
ejpam-3422	133	20	,	,	PUNCT
ejpam-3422	133	21	1	1	NUM
ejpam-3422	133	22	]	]	PUNCT
ejpam-3422	133	23	.	.	PUNCT
ejpam-3422	134	1	it	it	PRON
ejpam-3422	134	2	can	can	AUX
ejpam-3422	134	3	be	be	AUX
ejpam-3422	134	4	shown	show	VERB
ejpam-3422	134	5	that	that	SCONJ
ejpam-3422	134	6	µ	µ	NOUN
ejpam-3422	134	7	is	be	AUX
ejpam-3422	134	8	a	a	DET
ejpam-3422	134	9	fuzzy	fuzzy	ADJ
ejpam-3422	134	10	implicative	implicative	ADJ
ejpam-3422	134	11	hyper	hyper	ADJ
ejpam-3422	134	12	gr	gr	NOUN
ejpam-3422	134	13	-	-	PUNCT
ejpam-3422	134	14	ideal	ideal	NOUN
ejpam-3422	134	15	of	of	ADP
ejpam-3422	134	16	type	type	NOUN
ejpam-3422	134	17	1	1	NUM
ejpam-3422	134	18	in	in	ADP
ejpam-3422	134	19	h.	h.	PROPN
ejpam-3422	134	20	definition	definition	NOUN
ejpam-3422	134	21	4.3	4.3	NUM
ejpam-3422	134	22	.	.	PUNCT
ejpam-3422	135	1	a	a	DET
ejpam-3422	135	2	fuzzy	fuzzy	ADJ
ejpam-3422	135	3	set	set	VERB
ejpam-3422	135	4	µ	µ	NOUN
ejpam-3422	135	5	in	in	ADP
ejpam-3422	135	6	h	h	NOUN
ejpam-3422	135	7	is	be	AUX
ejpam-3422	135	8	called	call	VERB
ejpam-3422	135	9	a	a	DET
ejpam-3422	135	10	fuzzy	fuzzy	ADJ
ejpam-3422	135	11	implicative	implicative	ADJ
ejpam-3422	135	12	hyper	hyper	ADJ
ejpam-3422	135	13	gr	gr	NOUN
ejpam-3422	135	14	-	-	PUNCT
ejpam-3422	135	15	ideal	ideal	NOUN
ejpam-3422	135	16	of	of	ADP
ejpam-3422	135	17	type	type	NOUN
ejpam-3422	135	18	2	2	NUM
ejpam-3422	135	19	in	in	ADP
ejpam-3422	135	20	h	h	NOUN
ejpam-3422	135	21	if	if	SCONJ
ejpam-3422	135	22	fim1	fim1	NOUN
ejpam-3422	135	23	holds	hold	VERB
ejpam-3422	135	24	and	and	CCONJ
ejpam-3422	135	25	a.	a.	NOUN
ejpam-3422	135	26	macodi	macodi	NOUN
ejpam-3422	135	27	-	-	PUNCT
ejpam-3422	135	28	ringia	ringia	ADJ
ejpam-3422	135	29	,	,	PUNCT
ejpam-3422	135	30	g.	g.	PROPN
ejpam-3422	135	31	petalcorin	petalcorin	PROPN
ejpam-3422	135	32	,	,	PUNCT
ejpam-3422	135	33	jr	jr	PROPN
ejpam-3422	135	34	.	.	PROPN
ejpam-3422	135	35	/	/	SYM
ejpam-3422	135	36	eur	eur	PROPN
ejpam-3422	135	37	.	.	PUNCT
ejpam-3422	136	1	j.	j.	PROPN
ejpam-3422	136	2	pure	pure	PROPN
ejpam-3422	136	3	appl	appl	PROPN
ejpam-3422	136	4	.	.	PROPN
ejpam-3422	136	5	math	math	PROPN
ejpam-3422	136	6	,	,	PUNCT
ejpam-3422	136	7	12	12	NUM
ejpam-3422	136	8	(	(	PUNCT
ejpam-3422	136	9	2	2	NUM
ejpam-3422	136	10	)	)	PUNCT
ejpam-3422	136	11	(	(	PUNCT
ejpam-3422	136	12	2019	2019	NUM
ejpam-3422	136	13	)	)	PUNCT
ejpam-3422	136	14	,	,	PUNCT
ejpam-3422	136	15	409	409	NUM
ejpam-3422	136	16	-	-	SYM
ejpam-3422	136	17	417	417	NUM
ejpam-3422	136	18	415	415	NUM
ejpam-3422	136	19	(	(	PUNCT
ejpam-3422	136	20	fim2	fim2	PROPN
ejpam-3422	136	21	)	)	PUNCT
ejpam-3422	136	22	for	for	ADP
ejpam-3422	136	23	any	any	DET
ejpam-3422	136	24	x	x	NOUN
ejpam-3422	136	25	,	,	PUNCT
ejpam-3422	136	26	y	y	PROPN
ejpam-3422	136	27	,	,	PUNCT
ejpam-3422	136	28	z	z	PROPN
ejpam-3422	136	29	∈	∈	PROPN
ejpam-3422	136	30	h	h	NOUN
ejpam-3422	136	31	such	such	ADJ
ejpam-3422	136	32	that	that	SCONJ
ejpam-3422	136	33	x	x	PUNCT
ejpam-3422	136	34	�	�	PROPN
ejpam-3422	136	35	y	y	PROPN
ejpam-3422	136	36	,	,	PUNCT
ejpam-3422	136	37	we	we	PRON
ejpam-3422	136	38	have	have	VERB
ejpam-3422	136	39	µ(y	µ(y	NOUN
ejpam-3422	136	40	)	)	PUNCT
ejpam-3422	136	41	≤	≤	NOUN
ejpam-3422	136	42	µ(x	µ(x	NOUN
ejpam-3422	136	43	)	)	PUNCT
ejpam-3422	136	44	.	.	PUNCT
ejpam-3422	137	1	example	example	NOUN
ejpam-3422	137	2	4.4	4.4	NUM
ejpam-3422	137	3	.	.	PUNCT
ejpam-3422	138	1	consider	consider	VERB
ejpam-3422	138	2	the	the	DET
ejpam-3422	138	3	hyper	hyper	ADJ
ejpam-3422	138	4	gr	gr	NOUN
ejpam-3422	138	5	-	-	PUNCT
ejpam-3422	138	6	algebra	algebra	NOUN
ejpam-3422	138	7	h	h	NOUN
ejpam-3422	139	1	=	=	PUNCT
ejpam-3422	140	1	[	[	X
ejpam-3422	140	2	0	0	NUM
ejpam-3422	140	3	,	,	PUNCT
ejpam-3422	140	4	1	1	NUM
ejpam-3422	140	5	]	]	PUNCT
ejpam-3422	140	6	in	in	ADP
ejpam-3422	140	7	example	example	NOUN
ejpam-3422	140	8	4.2	4.2	NUM
ejpam-3422	140	9	.	.	PUNCT
ejpam-3422	140	10	note	note	VERB
ejpam-3422	140	11	that	that	SCONJ
ejpam-3422	140	12	from	from	ADP
ejpam-3422	140	13	fim2	fim2	PROPN
ejpam-3422	140	14	0	0	NUM
ejpam-3422	141	1	6=	6=	NUM
ejpam-3422	141	2	x	x	SYM
ejpam-3422	141	3	�	�	PROPN
ejpam-3422	141	4	y	y	PROPN
ejpam-3422	141	5	6=	6=	PROPN
ejpam-3422	141	6	0	0	NUM
ejpam-3422	141	7	and	and	CCONJ
ejpam-3422	141	8	0	0	NUM
ejpam-3422	141	9	6=	6=	NUM
ejpam-3422	141	10	y	y	PROPN
ejpam-3422	141	11	�	�	PROPN
ejpam-3422	141	12	x	x	PUNCT
ejpam-3422	141	13	6=	6=	ADP
ejpam-3422	141	14	0	0	NUM
ejpam-3422	141	15	for	for	ADP
ejpam-3422	141	16	x	x	X
ejpam-3422	141	17	,	,	PUNCT
ejpam-3422	141	18	y	y	PROPN
ejpam-3422	141	19	∈	∈	PROPN
ejpam-3422	141	20	h	h	NOUN
ejpam-3422	141	21	such	such	ADJ
ejpam-3422	141	22	that	that	SCONJ
ejpam-3422	141	23	x	x	SYM
ejpam-3422	141	24	6=	6=	NUM
ejpam-3422	141	25	y	y	PRON
ejpam-3422	141	26	should	should	AUX
ejpam-3422	141	27	imply	imply	VERB
ejpam-3422	141	28	to	to	ADP
ejpam-3422	141	29	µ(x	µ(x	NOUN
ejpam-3422	141	30	)	)	PUNCT
ejpam-3422	141	31	=	=	SYM
ejpam-3422	141	32	µ(y	µ(y	PROPN
ejpam-3422	141	33	)	)	PUNCT
ejpam-3422	141	34	.	.	PUNCT
ejpam-3422	142	1	on	on	ADP
ejpam-3422	142	2	the	the	DET
ejpam-3422	142	3	contrary	contrary	NOUN
ejpam-3422	142	4	,	,	PUNCT
ejpam-3422	142	5	the	the	DET
ejpam-3422	142	6	µ	µ	NOUN
ejpam-3422	142	7	in	in	ADP
ejpam-3422	142	8	example	example	NOUN
ejpam-3422	142	9	4.2	4.2	NUM
ejpam-3422	142	10	does	do	AUX
ejpam-3422	142	11	not	not	PART
ejpam-3422	142	12	give	give	VERB
ejpam-3422	142	13	µ(x	µ(x	NOUN
ejpam-3422	142	14	)	)	PUNCT
ejpam-3422	142	15	=	=	SYM
ejpam-3422	142	16	µ(y	µ(y	NOUN
ejpam-3422	142	17	)	)	PUNCT
ejpam-3422	142	18	whenever	whenever	SCONJ
ejpam-3422	142	19	x	x	X
ejpam-3422	142	20	6=	6=	ADP
ejpam-3422	142	21	y	y	PROPN
ejpam-3422	142	22	for	for	ADP
ejpam-3422	142	23	x	x	PROPN
ejpam-3422	142	24	,	,	PUNCT
ejpam-3422	142	25	y	y	PROPN
ejpam-3422	142	26	∈	∈	PROPN
ejpam-3422	142	27	h.	h.	PROPN
ejpam-3422	142	28	hence	hence	ADV
ejpam-3422	142	29	,	,	PUNCT
ejpam-3422	142	30	µ	µ	X
ejpam-3422	142	31	is	be	AUX
ejpam-3422	142	32	not	not	PART
ejpam-3422	142	33	a	a	DET
ejpam-3422	142	34	fuzzy	fuzzy	ADJ
ejpam-3422	142	35	implicative	implicative	ADJ
ejpam-3422	142	36	hyper	hyper	ADJ
ejpam-3422	142	37	gr	gr	NOUN
ejpam-3422	142	38	-	-	PUNCT
ejpam-3422	142	39	ideal	ideal	NOUN
ejpam-3422	142	40	of	of	ADP
ejpam-3422	142	41	type	type	NOUN
ejpam-3422	142	42	2	2	NUM
ejpam-3422	142	43	.	.	PUNCT
ejpam-3422	142	44	however	however	ADV
ejpam-3422	142	45	,	,	PUNCT
ejpam-3422	142	46	redefining	redefine	VERB
ejpam-3422	142	47	fuzzy	fuzzy	ADJ
ejpam-3422	142	48	set	set	VERB
ejpam-3422	142	49	µ	µ	NOUN
ejpam-3422	142	50	in	in	ADP
ejpam-3422	142	51	h	h	NOUN
ejpam-3422	142	52	by	by	ADP
ejpam-3422	142	53	µ(x	µ(x	NOUN
ejpam-3422	142	54	)	)	PUNCT
ejpam-3422	142	55	=	=	SYM
ejpam-3422	142	56	{	{	PUNCT
ejpam-3422	142	57	n	n	CCONJ
ejpam-3422	142	58	,	,	PUNCT
ejpam-3422	142	59	if	if	SCONJ
ejpam-3422	142	60	x	x	ADP
ejpam-3422	142	61	=	=	SYM
ejpam-3422	142	62	0	0	NUM
ejpam-3422	142	63	,	,	PUNCT
ejpam-3422	142	64	m	m	PRON
ejpam-3422	142	65	,	,	PUNCT
ejpam-3422	142	66	if	if	SCONJ
ejpam-3422	142	67	x	x	PROPN
ejpam-3422	142	68	6=	6=	ADP
ejpam-3422	142	69	0	0	NUM
ejpam-3422	142	70	,	,	PUNCT
ejpam-3422	142	71	where	where	SCONJ
ejpam-3422	142	72	m	m	VERB
ejpam-3422	142	73	,	,	PUNCT
ejpam-3422	142	74	n	n	PRON
ejpam-3422	142	75	∈	∈	NOUN
ejpam-3422	143	1	[	[	X
ejpam-3422	143	2	0	0	NUM
ejpam-3422	143	3	,	,	PUNCT
ejpam-3422	143	4	1	1	NUM
ejpam-3422	143	5	]	]	PUNCT
ejpam-3422	143	6	and	and	CCONJ
ejpam-3422	143	7	m	m	PRON
ejpam-3422	143	8	<	<	X
ejpam-3422	143	9	n	n	PRON
ejpam-3422	143	10	will	will	AUX
ejpam-3422	143	11	provide	provide	VERB
ejpam-3422	143	12	a	a	DET
ejpam-3422	143	13	fuzzy	fuzzy	ADJ
ejpam-3422	143	14	implicative	implicative	ADJ
ejpam-3422	143	15	hyper	hyper	ADJ
ejpam-3422	143	16	gr	gr	NOUN
ejpam-3422	143	17	-	-	PUNCT
ejpam-3422	143	18	ideal	ideal	NOUN
ejpam-3422	143	19	of	of	ADP
ejpam-3422	143	20	type	type	NOUN
ejpam-3422	143	21	2	2	NUM
ejpam-3422	143	22	µ	µ	NOUN
ejpam-3422	143	23	in	in	ADP
ejpam-3422	143	24	h	h	NOUN
ejpam-3422	143	25	.	.	PUNCT
ejpam-3422	144	1	it	it	PRON
ejpam-3422	144	2	can	can	AUX
ejpam-3422	144	3	be	be	AUX
ejpam-3422	144	4	seen	see	VERB
ejpam-3422	144	5	that	that	SCONJ
ejpam-3422	144	6	this	this	PRON
ejpam-3422	144	7	is	be	AUX
ejpam-3422	144	8	true	true	ADJ
ejpam-3422	144	9	by	by	ADP
ejpam-3422	144	10	routine	routine	ADJ
ejpam-3422	144	11	calculation	calculation	NOUN
ejpam-3422	144	12	.	.	PUNCT
ejpam-3422	145	1	example	example	NOUN
ejpam-3422	145	2	4.5	4.5	NUM
ejpam-3422	145	3	.	.	PUNCT
ejpam-3422	146	1	consider	consider	VERB
ejpam-3422	146	2	the	the	DET
ejpam-3422	146	3	hyper	hyper	ADJ
ejpam-3422	146	4	gr	gr	NOUN
ejpam-3422	146	5	-	-	PUNCT
ejpam-3422	146	6	algebra	algebra	NOUN
ejpam-3422	146	7	h	h	NOUN
ejpam-3422	146	8	in	in	ADP
ejpam-3422	146	9	example	example	NOUN
ejpam-3422	146	10	3.6	3.6	NUM
ejpam-3422	146	11	.	.	PUNCT
ejpam-3422	147	1	define	define	VERB
ejpam-3422	147	2	a	a	DET
ejpam-3422	147	3	fuzzy	fuzzy	ADJ
ejpam-3422	147	4	set	set	VERB
ejpam-3422	147	5	µ	µ	NOUN
ejpam-3422	147	6	in	in	ADP
ejpam-3422	147	7	h	h	NOUN
ejpam-3422	147	8	by	by	ADP
ejpam-3422	147	9	µ(1	µ(1	NOUN
ejpam-3422	147	10	)	)	PUNCT
ejpam-3422	147	11	=	=	NOUN
ejpam-3422	147	12	0.1	0.1	NUM
ejpam-3422	147	13	,	,	PUNCT
ejpam-3422	147	14	µ(2	µ(2	PROPN
ejpam-3422	147	15	)	)	PUNCT
ejpam-3422	147	16	=	=	NUM
ejpam-3422	147	17	0.2	0.2	NUM
ejpam-3422	147	18	and	and	CCONJ
ejpam-3422	147	19	µ(0	µ(0	NUM
ejpam-3422	147	20	)	)	PUNCT
ejpam-3422	147	21	=	=	PUNCT
ejpam-3422	147	22	0.3	0.3	NUM
ejpam-3422	147	23	.	.	PUNCT
ejpam-3422	148	1	by	by	ADP
ejpam-3422	148	2	routine	routine	ADJ
ejpam-3422	148	3	calculations	calculation	NOUN
ejpam-3422	148	4	,	,	PUNCT
ejpam-3422	148	5	we	we	PRON
ejpam-3422	148	6	see	see	VERB
ejpam-3422	148	7	that	that	SCONJ
ejpam-3422	148	8	µ	µ	NOUN
ejpam-3422	148	9	is	be	AUX
ejpam-3422	148	10	a	a	DET
ejpam-3422	148	11	fuzzy	fuzzy	ADJ
ejpam-3422	148	12	implicative	implicative	ADJ
ejpam-3422	148	13	hyper	hyper	ADJ
ejpam-3422	148	14	gr	gr	NOUN
ejpam-3422	148	15	-	-	PUNCT
ejpam-3422	148	16	ideal	ideal	NOUN
ejpam-3422	148	17	of	of	ADP
ejpam-3422	148	18	type	type	NOUN
ejpam-3422	148	19	2	2	NUM
ejpam-3422	148	20	in	in	ADP
ejpam-3422	148	21	h.	h.	PROPN
ejpam-3422	148	22	remark	remark	PROPN
ejpam-3422	148	23	4.6	4.6	NUM
ejpam-3422	148	24	.	.	PUNCT
ejpam-3422	149	1	from	from	ADP
ejpam-3422	149	2	definitions	definition	NOUN
ejpam-3422	149	3	4.1	4.1	NUM
ejpam-3422	149	4	and	and	CCONJ
ejpam-3422	149	5	4.3	4.3	NUM
ejpam-3422	149	6	,	,	PUNCT
ejpam-3422	149	7	it	it	PRON
ejpam-3422	149	8	shows	show	VERB
ejpam-3422	149	9	that	that	SCONJ
ejpam-3422	149	10	every	every	DET
ejpam-3422	149	11	fuzzy	fuzzy	ADJ
ejpam-3422	149	12	implicative	implicative	ADJ
ejpam-3422	149	13	hyper	hyper	ADJ
ejpam-3422	149	14	gr	gr	NOUN
ejpam-3422	149	15	-	-	PUNCT
ejpam-3422	149	16	ideal	ideal	NOUN
ejpam-3422	149	17	of	of	ADP
ejpam-3422	149	18	type	type	NOUN
ejpam-3422	149	19	2	2	NUM
ejpam-3422	149	20	is	be	AUX
ejpam-3422	149	21	a	a	DET
ejpam-3422	149	22	fuzzy	fuzzy	ADJ
ejpam-3422	149	23	implicative	implicative	ADJ
ejpam-3422	149	24	hyper	hyper	ADJ
ejpam-3422	149	25	gr	gr	NOUN
ejpam-3422	149	26	-	-	PUNCT
ejpam-3422	149	27	ideal	ideal	NOUN
ejpam-3422	149	28	of	of	ADP
ejpam-3422	149	29	type	type	NOUN
ejpam-3422	149	30	1	1	NUM
ejpam-3422	149	31	.	.	PUNCT
ejpam-3422	149	32	example	example	NOUN
ejpam-3422	149	33	4.4	4.4	NUM
ejpam-3422	149	34	shows	show	VERB
ejpam-3422	149	35	that	that	SCONJ
ejpam-3422	149	36	not	not	PART
ejpam-3422	149	37	all	all	PRON
ejpam-3422	149	38	fuzzy	fuzzy	ADJ
ejpam-3422	149	39	implicative	implicative	ADJ
ejpam-3422	149	40	hyper	hyper	ADJ
ejpam-3422	149	41	gr	gr	NOUN
ejpam-3422	149	42	-	-	PUNCT
ejpam-3422	149	43	ideal	ideal	NOUN
ejpam-3422	149	44	of	of	ADP
ejpam-3422	149	45	type	type	NOUN
ejpam-3422	149	46	1	1	NUM
ejpam-3422	149	47	is	be	AUX
ejpam-3422	149	48	a	a	DET
ejpam-3422	149	49	fuzzy	fuzzy	ADJ
ejpam-3422	149	50	implicative	implicative	ADJ
ejpam-3422	149	51	hyper	hyper	ADJ
ejpam-3422	149	52	gr	gr	NOUN
ejpam-3422	149	53	-	-	PUNCT
ejpam-3422	149	54	ideal	ideal	NOUN
ejpam-3422	149	55	of	of	ADP
ejpam-3422	149	56	type	type	NOUN
ejpam-3422	149	57	2	2	NUM
ejpam-3422	149	58	.	.	PUNCT
ejpam-3422	149	59	theorem	theorem	NOUN
ejpam-3422	149	60	4.7	4.7	NUM
ejpam-3422	149	61	.	.	PUNCT
ejpam-3422	150	1	a	a	DET
ejpam-3422	150	2	fuzzy	fuzzy	ADJ
ejpam-3422	150	3	set	set	VERB
ejpam-3422	150	4	µ	µ	NOUN
ejpam-3422	150	5	in	in	ADP
ejpam-3422	150	6	a	a	DET
ejpam-3422	150	7	hyper	hyper	ADJ
ejpam-3422	150	8	gr	gr	NOUN
ejpam-3422	150	9	-	-	PUNCT
ejpam-3422	150	10	algebra	algebra	NOUN
ejpam-3422	150	11	h	h	NOUN
ejpam-3422	150	12	is	be	AUX
ejpam-3422	150	13	a	a	DET
ejpam-3422	150	14	fuzzy	fuzzy	ADJ
ejpam-3422	150	15	implicative	implicative	ADJ
ejpam-3422	150	16	hyper	hyper	ADJ
ejpam-3422	150	17	grideal	grideal	NOUN
ejpam-3422	150	18	of	of	ADP
ejpam-3422	150	19	type	type	NOUN
ejpam-3422	150	20	1	1	NUM
ejpam-3422	150	21	if	if	SCONJ
ejpam-3422	150	22	and	and	CCONJ
ejpam-3422	150	23	only	only	ADV
ejpam-3422	150	24	if	if	SCONJ
ejpam-3422	150	25	µt	µt	PRON
ejpam-3422	150	26	is	be	AUX
ejpam-3422	150	27	an	an	DET
ejpam-3422	150	28	implicative	implicative	ADJ
ejpam-3422	150	29	hyper	hyper	ADJ
ejpam-3422	150	30	gr	gr	NOUN
ejpam-3422	150	31	-	-	PUNCT
ejpam-3422	150	32	ideal	ideal	NOUN
ejpam-3422	150	33	of	of	ADP
ejpam-3422	150	34	h	h	NOUN
ejpam-3422	151	1	whenever	whenever	SCONJ
ejpam-3422	151	2	µt	µt	PROPN
ejpam-3422	151	3	6=	6=	PROPN
ejpam-3422	151	4	φ	φ	PROPN
ejpam-3422	151	5	and	and	CCONJ
ejpam-3422	151	6	t	t	PROPN
ejpam-3422	151	7	∈	∈	PROPN
ejpam-3422	152	1	[	[	X
ejpam-3422	152	2	0	0	NUM
ejpam-3422	152	3	,	,	PUNCT
ejpam-3422	152	4	1	1	NUM
ejpam-3422	152	5	]	]	PUNCT
ejpam-3422	152	6	.	.	PUNCT
ejpam-3422	153	1	proof	proof	NOUN
ejpam-3422	153	2	.	.	PUNCT
ejpam-3422	154	1	suppose	suppose	VERB
ejpam-3422	154	2	µ	µ	PRON
ejpam-3422	154	3	is	be	AUX
ejpam-3422	154	4	a	a	DET
ejpam-3422	154	5	fuzzy	fuzzy	ADJ
ejpam-3422	154	6	implicative	implicative	ADJ
ejpam-3422	154	7	hyper	hyper	ADJ
ejpam-3422	154	8	gr	gr	NOUN
ejpam-3422	154	9	-	-	PUNCT
ejpam-3422	154	10	ideal	ideal	NOUN
ejpam-3422	154	11	of	of	ADP
ejpam-3422	154	12	type	type	NOUN
ejpam-3422	154	13	1	1	NUM
ejpam-3422	154	14	and	and	CCONJ
ejpam-3422	154	15	µt	µt	PRON
ejpam-3422	154	16	6=	6=	NUM
ejpam-3422	154	17	φ	φ	PROPN
ejpam-3422	154	18	.	.	PUNCT
ejpam-3422	155	1	let	let	VERB
ejpam-3422	155	2	t	t	PROPN
ejpam-3422	155	3	∈	∈	PROPN
ejpam-3422	156	1	[	[	X
ejpam-3422	156	2	0	0	NUM
ejpam-3422	156	3	,	,	PUNCT
ejpam-3422	156	4	1	1	NUM
ejpam-3422	156	5	]	]	PUNCT
ejpam-3422	156	6	.	.	PUNCT
ejpam-3422	157	1	since	since	SCONJ
ejpam-3422	157	2	µt	µt	PROPN
ejpam-3422	157	3	6=	6=	PROPN
ejpam-3422	157	4	φ	φ	NUM
ejpam-3422	157	5	,	,	PUNCT
ejpam-3422	157	6	there	there	PRON
ejpam-3422	157	7	exist	exist	VERB
ejpam-3422	157	8	x	x	SYM
ejpam-3422	157	9	∈	∈	PROPN
ejpam-3422	157	10	µt	µt	PROPN
ejpam-3422	157	11	.	.	PUNCT
ejpam-3422	157	12	by	by	ADP
ejpam-3422	157	13	fim1	fim1	NOUN
ejpam-3422	157	14	,	,	PUNCT
ejpam-3422	157	15	µ(0	µ(0	NOUN
ejpam-3422	157	16	)	)	PUNCT
ejpam-3422	157	17	≥	≥	NOUN
ejpam-3422	157	18	µ(x	µ(x	NOUN
ejpam-3422	157	19	)	)	PUNCT
ejpam-3422	157	20	≥	≥	NOUN
ejpam-3422	157	21	t.	t.	NOUN
ejpam-3422	158	1	it	it	PRON
ejpam-3422	158	2	follows	follow	VERB
ejpam-3422	158	3	that	that	SCONJ
ejpam-3422	158	4	0	0	NUM
ejpam-3422	158	5	∈	∈	PROPN
ejpam-3422	158	6	µt	µt	PROPN
ejpam-3422	158	7	.	.	PUNCT
ejpam-3422	159	1	let	let	VERB
ejpam-3422	159	2	x	x	PRON
ejpam-3422	159	3	,	,	PUNCT
ejpam-3422	159	4	y	y	PROPN
ejpam-3422	159	5	,	,	PUNCT
ejpam-3422	159	6	z	z	PROPN
ejpam-3422	159	7	∈	∈	PROPN
ejpam-3422	159	8	h	h	NOUN
ejpam-3422	159	9	such	such	ADJ
ejpam-3422	159	10	that	that	SCONJ
ejpam-3422	159	11	(	(	PUNCT
ejpam-3422	159	12	x	x	X
ejpam-3422	159	13	~	~	PUNCT
ejpam-3422	159	14	z	z	X
ejpam-3422	159	15	)	)	PUNCT
ejpam-3422	159	16	~	~	PUNCT
ejpam-3422	159	17	(	(	PUNCT
ejpam-3422	159	18	y	y	X
ejpam-3422	159	19	~	~	PUNCT
ejpam-3422	159	20	x	x	X
ejpam-3422	159	21	)	)	PUNCT
ejpam-3422	160	1	⊆	⊆	NUM
ejpam-3422	160	2	µt	µt	NOUN
ejpam-3422	160	3	and	and	CCONJ
ejpam-3422	160	4	z	z	PROPN
ejpam-3422	160	5	∈	∈	PROPN
ejpam-3422	161	1	µt	µt	PROPN
ejpam-3422	161	2	.	.	PUNCT
ejpam-3422	161	3	then	then	ADV
ejpam-3422	161	4	µ(z	µ(z	PROPN
ejpam-3422	161	5	)	)	PUNCT
ejpam-3422	161	6	≥	≥	NOUN
ejpam-3422	161	7	t	t	NOUN
ejpam-3422	161	8	and	and	CCONJ
ejpam-3422	161	9	µ(u	µ(u	NOUN
ejpam-3422	161	10	)	)	PUNCT
ejpam-3422	161	11	≥	≥	NOUN
ejpam-3422	161	12	t	t	NOUN
ejpam-3422	161	13	for	for	ADP
ejpam-3422	161	14	any	any	DET
ejpam-3422	161	15	u	u	NOUN
ejpam-3422	161	16	∈	∈	PROPN
ejpam-3422	161	17	(	(	PUNCT
ejpam-3422	161	18	x	x	X
ejpam-3422	161	19	~	~	PUNCT
ejpam-3422	161	20	z	z	X
ejpam-3422	161	21	)	)	PUNCT
ejpam-3422	161	22	~	~	PUNCT
ejpam-3422	161	23	(	(	PUNCT
ejpam-3422	161	24	y	y	X
ejpam-3422	161	25	~	~	PUNCT
ejpam-3422	161	26	x	x	X
ejpam-3422	161	27	)	)	PUNCT
ejpam-3422	161	28	.	.	PUNCT
ejpam-3422	162	1	this	this	PRON
ejpam-3422	162	2	implies	imply	VERB
ejpam-3422	162	3	that	that	SCONJ
ejpam-3422	162	4	t	t	PROPN
ejpam-3422	162	5	is	be	AUX
ejpam-3422	162	6	a	a	DET
ejpam-3422	162	7	lowerbound	lowerbound	NOUN
ejpam-3422	162	8	for	for	ADP
ejpam-3422	162	9	the	the	DET
ejpam-3422	162	10	set	set	NOUN
ejpam-3422	162	11	{	{	PUNCT
ejpam-3422	162	12	µ(u)|u	µ(u)|u	PROPN
ejpam-3422	162	13	∈	∈	PROPN
ejpam-3422	162	14	(	(	PUNCT
ejpam-3422	162	15	x~	x~	PROPN
ejpam-3422	162	16	z	z	PROPN
ejpam-3422	162	17	)	)	PUNCT
ejpam-3422	162	18	~	~	PUNCT
ejpam-3422	162	19	(	(	PUNCT
ejpam-3422	162	20	y	y	X
ejpam-3422	162	21	~	~	PUNCT
ejpam-3422	162	22	x	x	X
ejpam-3422	162	23	)	)	PUNCT
ejpam-3422	162	24	}	}	PUNCT
ejpam-3422	162	25	.	.	PUNCT
ejpam-3422	163	1	then	then	ADV
ejpam-3422	163	2	,	,	PUNCT
ejpam-3422	163	3	inf	inf	PROPN
ejpam-3422	163	4	u∈(x	u∈(x	PROPN
ejpam-3422	163	5	~	~	SYM
ejpam-3422	163	6	z)~(y	z)~(y	PROPN
ejpam-3422	163	7	~	~	SYM
ejpam-3422	163	8	x	x	X
ejpam-3422	163	9	)	)	PUNCT
ejpam-3422	163	10	µ(u	µ(u	NOUN
ejpam-3422	163	11	)	)	PUNCT
ejpam-3422	163	12	≥	≥	NOUN
ejpam-3422	163	13	t.	t.	NOUN
ejpam-3422	163	14	by	by	ADP
ejpam-3422	163	15	fim1	fim1	PROPN
ejpam-3422	163	16	,	,	PUNCT
ejpam-3422	163	17	µ(x	µ(x	NOUN
ejpam-3422	163	18	)	)	PUNCT
ejpam-3422	163	19	≥	≥	NOUN
ejpam-3422	163	20	min	min	PROPN
ejpam-3422	163	21	{	{	PUNCT
ejpam-3422	163	22	inf	inf	NOUN
ejpam-3422	163	23	u∈(x	u∈(x	PROPN
ejpam-3422	163	24	~	~	SYM
ejpam-3422	163	25	z)~(y	z)~(y	PROPN
ejpam-3422	163	26	~	~	SYM
ejpam-3422	163	27	x	x	X
ejpam-3422	163	28	)	)	PUNCT
ejpam-3422	163	29	µ(u	µ(u	NOUN
ejpam-3422	163	30	)	)	PUNCT
ejpam-3422	163	31	,	,	PUNCT
ejpam-3422	163	32	µ(z	µ(z	PROPN
ejpam-3422	163	33	)	)	PUNCT
ejpam-3422	163	34	}	}	PUNCT
ejpam-3422	163	35	≥	≥	NOUN
ejpam-3422	163	36	min{t	min{t	PROPN
ejpam-3422	163	37	,	,	PUNCT
ejpam-3422	163	38	t	t	PROPN
ejpam-3422	163	39	}	}	PUNCT
ejpam-3422	163	40	=	=	SYM
ejpam-3422	163	41	t.	t.	NOUN
ejpam-3422	163	42	hence	hence	ADV
ejpam-3422	163	43	,	,	PUNCT
ejpam-3422	163	44	x	x	PUNCT
ejpam-3422	163	45	∈	∈	ADJ
ejpam-3422	163	46	µt	µt	X
ejpam-3422	163	47	and	and	CCONJ
ejpam-3422	163	48	so	so	ADV
ejpam-3422	163	49	µt	µt	PRON
ejpam-3422	163	50	is	be	AUX
ejpam-3422	163	51	implicative	implicative	ADJ
ejpam-3422	163	52	hyper	hyper	ADJ
ejpam-3422	163	53	gr	gr	NOUN
ejpam-3422	163	54	-	-	PUNCT
ejpam-3422	163	55	ideal	ideal	NOUN
ejpam-3422	163	56	of	of	ADP
ejpam-3422	163	57	h.	h.	NOUN
ejpam-3422	163	58	conversely	conversely	ADV
ejpam-3422	163	59	,	,	PUNCT
ejpam-3422	163	60	suppose	suppose	VERB
ejpam-3422	163	61	µt	µt	PRON
ejpam-3422	163	62	is	be	AUX
ejpam-3422	163	63	an	an	DET
ejpam-3422	163	64	implicative	implicative	ADJ
ejpam-3422	163	65	hyper	hyper	ADJ
ejpam-3422	163	66	gr	gr	NOUN
ejpam-3422	163	67	-	-	PUNCT
ejpam-3422	163	68	ideal	ideal	NOUN
ejpam-3422	163	69	of	of	ADP
ejpam-3422	163	70	h.	h.	PROPN
ejpam-3422	163	71	let	let	VERB
ejpam-3422	163	72	x	x	SYM
ejpam-3422	163	73	∈	∈	PROPN
ejpam-3422	163	74	h	h	NOUN
ejpam-3422	163	75	and	and	CCONJ
ejpam-3422	163	76	let	let	VERB
ejpam-3422	163	77	t	t	X
ejpam-3422	163	78	∈	∈	PROPN
ejpam-3422	164	1	[	[	X
ejpam-3422	164	2	0	0	NUM
ejpam-3422	164	3	,	,	PUNCT
ejpam-3422	164	4	1	1	NUM
ejpam-3422	164	5	]	]	PUNCT
ejpam-3422	164	6	such	such	ADJ
ejpam-3422	164	7	that	that	SCONJ
ejpam-3422	164	8	t	t	NOUN
ejpam-3422	164	9	=	=	PUNCT
ejpam-3422	164	10	µ(x	µ(x	X
ejpam-3422	164	11	)	)	PUNCT
ejpam-3422	164	12	.	.	PUNCT
ejpam-3422	165	1	since	since	SCONJ
ejpam-3422	165	2	0	0	NUM
ejpam-3422	165	3	∈	∈	PROPN
ejpam-3422	165	4	µt	µt	NOUN
ejpam-3422	165	5	,	,	PUNCT
ejpam-3422	165	6	µ(0	µ(0	PROPN
ejpam-3422	165	7	)	)	PUNCT
ejpam-3422	165	8	≥	≥	NOUN
ejpam-3422	165	9	t	t	NOUN
ejpam-3422	165	10	=	=	PUNCT
ejpam-3422	165	11	µ(x	µ(x	X
ejpam-3422	165	12	)	)	PUNCT
ejpam-3422	165	13	.	.	PUNCT
ejpam-3422	166	1	moreover	moreover	ADV
ejpam-3422	166	2	,	,	PUNCT
ejpam-3422	166	3	let	let	VERB
ejpam-3422	166	4	x	x	PRON
ejpam-3422	166	5	,	,	PUNCT
ejpam-3422	166	6	y	y	PROPN
ejpam-3422	166	7	,	,	PUNCT
ejpam-3422	166	8	z	z	PROPN
ejpam-3422	166	9	∈	∈	PROPN
ejpam-3422	166	10	h	h	NOUN
ejpam-3422	166	11	and	and	CCONJ
ejpam-3422	166	12	let	let	VERB
ejpam-3422	166	13	t	t	X
ejpam-3422	166	14	∈	∈	PROPN
ejpam-3422	167	1	[	[	X
ejpam-3422	167	2	0	0	NUM
ejpam-3422	167	3	,	,	PUNCT
ejpam-3422	167	4	1	1	NUM
ejpam-3422	167	5	]	]	PUNCT
ejpam-3422	167	6	such	such	ADJ
ejpam-3422	167	7	that	that	SCONJ
ejpam-3422	167	8	t	t	NOUN
ejpam-3422	167	9	=	=	SYM
ejpam-3422	167	10	min	min	PROPN
ejpam-3422	167	11	{	{	PUNCT
ejpam-3422	167	12	inf	inf	NOUN
ejpam-3422	167	13	u∈(x	u∈(x	PROPN
ejpam-3422	167	14	~	~	SYM
ejpam-3422	167	15	z)~(y	z)~(y	PROPN
ejpam-3422	167	16	~	~	SYM
ejpam-3422	167	17	x	x	X
ejpam-3422	167	18	)	)	PUNCT
ejpam-3422	167	19	µ(u	µ(u	NOUN
ejpam-3422	167	20	)	)	PUNCT
ejpam-3422	167	21	,	,	PUNCT
ejpam-3422	167	22	µ(z	µ(z	PROPN
ejpam-3422	167	23	)	)	PUNCT
ejpam-3422	167	24	}	}	PUNCT
ejpam-3422	167	25	.	.	PUNCT
ejpam-3422	168	1	since	since	SCONJ
ejpam-3422	168	2	µ(z	µ(z	PROPN
ejpam-3422	168	3	)	)	PUNCT
ejpam-3422	168	4	≥	≥	NOUN
ejpam-3422	168	5	min	min	PROPN
ejpam-3422	168	6	{	{	PUNCT
ejpam-3422	168	7	inf	inf	NOUN
ejpam-3422	168	8	u∈(x	u∈(x	PROPN
ejpam-3422	168	9	~	~	SYM
ejpam-3422	168	10	z)~(y	z)~(y	PROPN
ejpam-3422	168	11	~	~	SYM
ejpam-3422	168	12	x	x	X
ejpam-3422	168	13	)	)	PUNCT
ejpam-3422	168	14	µ(u	µ(u	NOUN
ejpam-3422	168	15	)	)	PUNCT
ejpam-3422	168	16	,	,	PUNCT
ejpam-3422	168	17	µ(z	µ(z	PROPN
ejpam-3422	168	18	)	)	PUNCT
ejpam-3422	168	19	}	}	PUNCT
ejpam-3422	168	20	=	=	SYM
ejpam-3422	168	21	t	t	PROPN
ejpam-3422	168	22	,	,	PUNCT
ejpam-3422	168	23	z	z	PROPN
ejpam-3422	168	24	∈	∈	PROPN
ejpam-3422	168	25	µt	µt	PROPN
ejpam-3422	168	26	.	.	PUNCT
ejpam-3422	168	27	let	let	VERB
ejpam-3422	168	28	v	v	X
ejpam-3422	168	29	∈	∈	NOUN
ejpam-3422	168	30	(	(	PUNCT
ejpam-3422	168	31	x	x	X
ejpam-3422	168	32	~	~	X
ejpam-3422	168	33	z)~(y	z)~(y	NOUN
ejpam-3422	168	34	~	~	SYM
ejpam-3422	168	35	x	x	X
ejpam-3422	168	36	)	)	PUNCT
ejpam-3422	168	37	.	.	PUNCT
ejpam-3422	169	1	then	then	ADV
ejpam-3422	169	2	µ(v	µ(v	PROPN
ejpam-3422	169	3	)	)	PUNCT
ejpam-3422	169	4	≥	≥	PROPN
ejpam-3422	169	5	inf	inf	PROPN
ejpam-3422	169	6	u∈(x	u∈(x	PROPN
ejpam-3422	169	7	~	~	SYM
ejpam-3422	169	8	z)~(y	z)~(y	PROPN
ejpam-3422	169	9	~	~	SYM
ejpam-3422	169	10	x	x	X
ejpam-3422	169	11	)	)	PUNCT
ejpam-3422	169	12	µ(u	µ(u	NOUN
ejpam-3422	169	13	)	)	PUNCT
ejpam-3422	169	14	≥	≥	PROPN
ejpam-3422	169	15	min	min	PROPN
ejpam-3422	169	16	{	{	PUNCT
ejpam-3422	169	17	inf	inf	NOUN
ejpam-3422	169	18	u∈(x	u∈(x	PROPN
ejpam-3422	169	19	~	~	SYM
ejpam-3422	169	20	z)~(y	z)~(y	PROPN
ejpam-3422	169	21	~	~	SYM
ejpam-3422	169	22	x	x	X
ejpam-3422	169	23	)	)	PUNCT
ejpam-3422	169	24	µ(u	µ(u	NOUN
ejpam-3422	169	25	)	)	PUNCT
ejpam-3422	169	26	,	,	PUNCT
ejpam-3422	169	27	µ(z	µ(z	PROPN
ejpam-3422	169	28	)	)	PUNCT
ejpam-3422	169	29	}	}	PUNCT
ejpam-3422	169	30	=	=	PUNCT
ejpam-3422	170	1	t.	t.	NOUN
ejpam-3422	170	2	then	then	ADV
ejpam-3422	170	3	v	v	ADP
ejpam-3422	170	4	∈	∈	PRON
ejpam-3422	170	5	µt	µt	X
ejpam-3422	170	6	and	and	CCONJ
ejpam-3422	170	7	hence	hence	ADV
ejpam-3422	170	8	(	(	PUNCT
ejpam-3422	170	9	x~	x~	PROPN
ejpam-3422	170	10	z	z	PROPN
ejpam-3422	170	11	)	)	PUNCT
ejpam-3422	170	12	~	~	PUNCT
ejpam-3422	170	13	(	(	PUNCT
ejpam-3422	170	14	y	y	X
ejpam-3422	170	15	~	~	PUNCT
ejpam-3422	170	16	x	x	X
ejpam-3422	170	17	)	)	PUNCT
ejpam-3422	170	18	⊂	⊂	PROPN
ejpam-3422	171	1	µt	µt	PROPN
ejpam-3422	171	2	.	.	PUNCT
ejpam-3422	172	1	since	since	SCONJ
ejpam-3422	172	2	µt	µt	PRON
ejpam-3422	172	3	is	be	AUX
ejpam-3422	172	4	implicative	implicative	ADJ
ejpam-3422	172	5	hyper	hyper	ADJ
ejpam-3422	172	6	gr	gr	NOUN
ejpam-3422	172	7	-	-	PUNCT
ejpam-3422	172	8	ideal	ideal	NOUN
ejpam-3422	172	9	,	,	PUNCT
ejpam-3422	172	10	x	x	SYM
ejpam-3422	172	11	∈	∈	PROPN
ejpam-3422	172	12	µt	µt	PROPN
ejpam-3422	172	13	.	.	PUNCT
ejpam-3422	172	14	thus	thus	ADV
ejpam-3422	172	15	µ(x	µ(x	NOUN
ejpam-3422	172	16	)	)	PUNCT
ejpam-3422	172	17	≥	≥	NOUN
ejpam-3422	172	18	t	t	NOUN
ejpam-3422	172	19	=	=	SYM
ejpam-3422	172	20	min	min	PROPN
ejpam-3422	172	21	{	{	PUNCT
ejpam-3422	172	22	inf	inf	NOUN
ejpam-3422	172	23	u∈(x	u∈(x	PROPN
ejpam-3422	172	24	~	~	SYM
ejpam-3422	172	25	z)~(y	z)~(y	PROPN
ejpam-3422	172	26	~	~	SYM
ejpam-3422	172	27	x	x	X
ejpam-3422	172	28	)	)	PUNCT
ejpam-3422	172	29	µ(u	µ(u	NOUN
ejpam-3422	172	30	)	)	PUNCT
ejpam-3422	172	31	,	,	PUNCT
ejpam-3422	172	32	µ(z	µ(z	PROPN
ejpam-3422	172	33	)	)	PUNCT
ejpam-3422	172	34	}	}	PUNCT
ejpam-3422	172	35	.	.	PUNCT
ejpam-3422	173	1	a.	a.	NOUN
ejpam-3422	173	2	macodi	macodi	PROPN
ejpam-3422	173	3	-	-	PUNCT
ejpam-3422	173	4	ringia	ringia	ADJ
ejpam-3422	173	5	,	,	PUNCT
ejpam-3422	173	6	g.	g.	PROPN
ejpam-3422	173	7	petalcorin	petalcorin	PROPN
ejpam-3422	173	8	,	,	PUNCT
ejpam-3422	173	9	jr	jr	PROPN
ejpam-3422	173	10	.	.	PROPN
ejpam-3422	173	11	/	/	SYM
ejpam-3422	173	12	eur	eur	PROPN
ejpam-3422	173	13	.	.	PUNCT
ejpam-3422	174	1	j.	j.	PROPN
ejpam-3422	174	2	pure	pure	PROPN
ejpam-3422	174	3	appl	appl	PROPN
ejpam-3422	174	4	.	.	PROPN
ejpam-3422	174	5	math	math	PROPN
ejpam-3422	174	6	,	,	PUNCT
ejpam-3422	174	7	12	12	NUM
ejpam-3422	174	8	(	(	PUNCT
ejpam-3422	174	9	2	2	NUM
ejpam-3422	174	10	)	)	PUNCT
ejpam-3422	174	11	(	(	PUNCT
ejpam-3422	174	12	2019	2019	NUM
ejpam-3422	174	13	)	)	PUNCT
ejpam-3422	174	14	,	,	PUNCT
ejpam-3422	174	15	409	409	NUM
ejpam-3422	174	16	-	-	SYM
ejpam-3422	174	17	417	417	NUM
ejpam-3422	174	18	416	416	NUM
ejpam-3422	174	19	theorem	theorem	NOUN
ejpam-3422	174	20	4.8	4.8	NUM
ejpam-3422	174	21	.	.	PUNCT
ejpam-3422	175	1	for	for	ADP
ejpam-3422	175	2	any	any	DET
ejpam-3422	175	3	nonempty	nonempty	NOUN
ejpam-3422	175	4	subset	subset	VERB
ejpam-3422	175	5	i	i	PRON
ejpam-3422	175	6	of	of	ADP
ejpam-3422	175	7	h	h	NOUN
ejpam-3422	175	8	,	,	PUNCT
ejpam-3422	175	9	let	let	VERB
ejpam-3422	175	10	µt	µt	PART
ejpam-3422	175	11	be	be	AUX
ejpam-3422	175	12	a	a	DET
ejpam-3422	175	13	fuzzy	fuzzy	ADJ
ejpam-3422	175	14	set	set	NOUN
ejpam-3422	175	15	in	in	ADP
ejpam-3422	175	16	h	h	NOUN
ejpam-3422	175	17	defined	define	VERB
ejpam-3422	175	18	by	by	ADP
ejpam-3422	175	19	µi(x	µi(x	NUM
ejpam-3422	175	20	)	)	PUNCT
ejpam-3422	176	1	=	=	PRON
ejpam-3422	176	2	{	{	PUNCT
ejpam-3422	176	3	k	k	NOUN
ejpam-3422	176	4	,	,	PUNCT
ejpam-3422	176	5	if	if	SCONJ
ejpam-3422	176	6	x	x	SYM
ejpam-3422	176	7	∈	∈	PROPN
ejpam-3422	176	8	i	i	NOUN
ejpam-3422	176	9	l	l	NOUN
ejpam-3422	176	10	,	,	PUNCT
ejpam-3422	176	11	otherwise	otherwise	ADV
ejpam-3422	176	12	,	,	PUNCT
ejpam-3422	176	13	for	for	ADP
ejpam-3422	176	14	all	all	DET
ejpam-3422	176	15	x	x	SYM
ejpam-3422	176	16	∈	∈	PROPN
ejpam-3422	176	17	h	h	NOUN
ejpam-3422	176	18	,	,	PUNCT
ejpam-3422	176	19	where	where	SCONJ
ejpam-3422	176	20	k	k	NOUN
ejpam-3422	176	21	,	,	PUNCT
ejpam-3422	176	22	l	l	PROPN
ejpam-3422	176	23	∈	∈	PROPN
ejpam-3422	177	1	[	[	X
ejpam-3422	177	2	0	0	NUM
ejpam-3422	177	3	,	,	PUNCT
ejpam-3422	177	4	1	1	NUM
ejpam-3422	177	5	]	]	PUNCT
ejpam-3422	177	6	with	with	ADP
ejpam-3422	177	7	k	k	PROPN
ejpam-3422	177	8	>	>	X
ejpam-3422	177	9	l.	l.	PROPN
ejpam-3422	178	1	then	then	ADV
ejpam-3422	178	2	i	i	PRON
ejpam-3422	178	3	is	be	AUX
ejpam-3422	178	4	an	an	DET
ejpam-3422	178	5	implicative	implicative	ADJ
ejpam-3422	178	6	hyper	hyper	ADJ
ejpam-3422	178	7	gr	gr	NOUN
ejpam-3422	178	8	-	-	PUNCT
ejpam-3422	178	9	ideal	ideal	NOUN
ejpam-3422	178	10	of	of	ADP
ejpam-3422	178	11	h	h	NOUN
ejpam-3422	178	12	if	if	SCONJ
ejpam-3422	179	1	and	and	CCONJ
ejpam-3422	179	2	only	only	ADV
ejpam-3422	179	3	if	if	SCONJ
ejpam-3422	179	4	µi	µi	PROPN
ejpam-3422	179	5	is	be	AUX
ejpam-3422	179	6	a	a	DET
ejpam-3422	179	7	fuzzy	fuzzy	ADJ
ejpam-3422	179	8	implicative	implicative	ADJ
ejpam-3422	179	9	hyper	hyper	ADJ
ejpam-3422	179	10	gr	gr	NOUN
ejpam-3422	179	11	-	-	PUNCT
ejpam-3422	179	12	ideal	ideal	NOUN
ejpam-3422	179	13	of	of	ADP
ejpam-3422	179	14	type	type	NOUN
ejpam-3422	179	15	1	1	NUM
ejpam-3422	179	16	in	in	ADP
ejpam-3422	179	17	h.	h.	NOUN
ejpam-3422	179	18	proof	proof	NOUN
ejpam-3422	179	19	.	.	PUNCT
ejpam-3422	180	1	note	note	VERB
ejpam-3422	180	2	that	that	SCONJ
ejpam-3422	180	3	(	(	PUNCT
ejpam-3422	180	4	µi)t	µi)t	PROPN
ejpam-3422	180	5	=	=	PUNCT
ejpam-3422	180	6			PUNCT
ejpam-3422	180	7	φ	φ	PROPN
ejpam-3422	180	8	,	,	PUNCT
ejpam-3422	180	9	if	if	SCONJ
ejpam-3422	180	10	k	k	PROPN
ejpam-3422	180	11	<	<	X
ejpam-3422	180	12	t	t	X
ejpam-3422	180	13	≤	≤	NUM
ejpam-3422	180	14	1	1	NUM
ejpam-3422	180	15	,	,	PUNCT
ejpam-3422	180	16	i	i	PRON
ejpam-3422	180	17	,	,	PUNCT
ejpam-3422	180	18	if	if	SCONJ
ejpam-3422	180	19	l	l	PROPN
ejpam-3422	180	20	<	<	X
ejpam-3422	180	21	t	t	X
ejpam-3422	180	22	≤	≤	NUM
ejpam-3422	181	1	k	k	PROPN
ejpam-3422	181	2	,	,	PUNCT
ejpam-3422	181	3	h	h	INTJ
ejpam-3422	181	4	,	,	PUNCT
ejpam-3422	181	5	if	if	SCONJ
ejpam-3422	181	6	0	0	NUM
ejpam-3422	181	7	≤	≤	NUM
ejpam-3422	181	8	t	t	PROPN
ejpam-3422	181	9	≤	≤	PROPN
ejpam-3422	181	10	l.	l.	PROPN
ejpam-3422	181	11	(	(	PUNCT
ejpam-3422	181	12	1	1	X
ejpam-3422	181	13	)	)	PUNCT
ejpam-3422	181	14	assume	assume	VERB
ejpam-3422	181	15	that	that	SCONJ
ejpam-3422	181	16	i	i	PRON
ejpam-3422	181	17	is	be	AUX
ejpam-3422	181	18	an	an	DET
ejpam-3422	181	19	implicative	implicative	ADJ
ejpam-3422	181	20	hyper	hyper	ADJ
ejpam-3422	181	21	gr	gr	NOUN
ejpam-3422	181	22	-	-	PUNCT
ejpam-3422	181	23	ideal	ideal	NOUN
ejpam-3422	181	24	of	of	ADP
ejpam-3422	181	25	h.	h.	PROPN
ejpam-3422	181	26	it	it	PRON
ejpam-3422	181	27	follows	follow	VERB
ejpam-3422	181	28	from	from	ADP
ejpam-3422	181	29	(	(	PUNCT
ejpam-3422	181	30	1	1	NUM
ejpam-3422	181	31	)	)	PUNCT
ejpam-3422	182	1	that	that	SCONJ
ejpam-3422	182	2	a	a	DET
ejpam-3422	182	3	nonempty	nonempty	NOUN
ejpam-3422	182	4	(	(	PUNCT
ejpam-3422	182	5	µi)t	µi)t	PROPN
ejpam-3422	182	6	is	be	AUX
ejpam-3422	182	7	an	an	DET
ejpam-3422	182	8	implicative	implicative	ADJ
ejpam-3422	182	9	hyper	hyper	ADJ
ejpam-3422	182	10	gr	gr	NOUN
ejpam-3422	182	11	-	-	PUNCT
ejpam-3422	182	12	ideal	ideal	NOUN
ejpam-3422	182	13	of	of	ADP
ejpam-3422	182	14	h	h	NOUN
ejpam-3422	182	15	for	for	ADP
ejpam-3422	182	16	all	all	DET
ejpam-3422	182	17	t	t	NOUN
ejpam-3422	182	18	∈	∈	PROPN
ejpam-3422	183	1	[	[	X
ejpam-3422	183	2	0	0	NUM
ejpam-3422	183	3	,	,	PUNCT
ejpam-3422	183	4	1	1	NUM
ejpam-3422	183	5	]	]	PUNCT
ejpam-3422	183	6	.	.	PUNCT
ejpam-3422	184	1	by	by	ADP
ejpam-3422	184	2	theorem	theorem	NOUN
ejpam-3422	184	3	4.7	4.7	NUM
ejpam-3422	184	4	,	,	PUNCT
ejpam-3422	184	5	µi	µi	PROPN
ejpam-3422	184	6	is	be	AUX
ejpam-3422	184	7	a	a	DET
ejpam-3422	184	8	fuzzy	fuzzy	ADJ
ejpam-3422	184	9	implicative	implicative	ADJ
ejpam-3422	184	10	hyper	hyper	ADJ
ejpam-3422	184	11	gr	gr	NOUN
ejpam-3422	184	12	-	-	PUNCT
ejpam-3422	184	13	ideal	ideal	NOUN
ejpam-3422	184	14	of	of	ADP
ejpam-3422	184	15	type	type	NOUN
ejpam-3422	184	16	1	1	NUM
ejpam-3422	184	17	in	in	ADP
ejpam-3422	184	18	h.	h.	NOUN
ejpam-3422	184	19	conversely	conversely	ADV
ejpam-3422	184	20	,	,	PUNCT
ejpam-3422	184	21	suppose	suppose	VERB
ejpam-3422	184	22	that	that	SCONJ
ejpam-3422	184	23	µi	µi	PROPN
ejpam-3422	184	24	is	be	AUX
ejpam-3422	184	25	a	a	DET
ejpam-3422	184	26	fuzzy	fuzzy	ADJ
ejpam-3422	184	27	implicative	implicative	ADJ
ejpam-3422	184	28	hyper	hyper	ADJ
ejpam-3422	184	29	gr	gr	NOUN
ejpam-3422	184	30	-	-	PUNCT
ejpam-3422	184	31	ideal	ideal	NOUN
ejpam-3422	184	32	of	of	ADP
ejpam-3422	184	33	type	type	NOUN
ejpam-3422	184	34	1	1	NUM
ejpam-3422	184	35	in	in	ADP
ejpam-3422	184	36	h.	h.	PROPN
ejpam-3422	184	37	by	by	ADP
ejpam-3422	184	38	theorem	theorem	NOUN
ejpam-3422	184	39	4.7	4.7	NUM
ejpam-3422	184	40	,	,	PUNCT
ejpam-3422	184	41	we	we	PRON
ejpam-3422	184	42	can	can	AUX
ejpam-3422	184	43	see	see	VERB
ejpam-3422	184	44	in	in	ADP
ejpam-3422	184	45	(	(	PUNCT
ejpam-3422	184	46	1	1	NUM
ejpam-3422	184	47	)	)	PUNCT
ejpam-3422	185	1	that	that	SCONJ
ejpam-3422	185	2	a	a	DET
ejpam-3422	185	3	nonempty	nonempty	NOUN
ejpam-3422	185	4	(	(	PUNCT
ejpam-3422	185	5	µi)t	µi)t	PROPN
ejpam-3422	185	6	is	be	AUX
ejpam-3422	185	7	an	an	DET
ejpam-3422	185	8	implicative	implicative	ADJ
ejpam-3422	185	9	hyper	hyper	ADJ
ejpam-3422	185	10	gr	gr	NOUN
ejpam-3422	185	11	-	-	PUNCT
ejpam-3422	185	12	ideal	ideal	NOUN
ejpam-3422	185	13	for	for	ADP
ejpam-3422	185	14	all	all	DET
ejpam-3422	185	15	t	t	NOUN
ejpam-3422	185	16	∈	∈	PROPN
ejpam-3422	186	1	[	[	X
ejpam-3422	186	2	0	0	NUM
ejpam-3422	186	3	,	,	PUNCT
ejpam-3422	186	4	1	1	NUM
ejpam-3422	186	5	]	]	PUNCT
ejpam-3422	187	1	and	and	CCONJ
ejpam-3422	187	2	so	so	ADV
ejpam-3422	187	3	i	i	PRON
ejpam-3422	187	4	is	be	AUX
ejpam-3422	187	5	an	an	DET
ejpam-3422	187	6	implicative	implicative	ADJ
ejpam-3422	187	7	hyper	hyper	ADJ
ejpam-3422	187	8	gr	gr	NOUN
ejpam-3422	187	9	-	-	PUNCT
ejpam-3422	187	10	ideal	ideal	NOUN
ejpam-3422	187	11	of	of	ADP
ejpam-3422	187	12	h.	h.	PROPN
ejpam-3422	187	13	theorem	theorem	PROPN
ejpam-3422	187	14	4.9	4.9	NUM
ejpam-3422	187	15	.	.	PUNCT
ejpam-3422	188	1	if	if	SCONJ
ejpam-3422	188	2	a	a	DET
ejpam-3422	188	3	fuzzy	fuzzy	ADJ
ejpam-3422	188	4	set	set	VERB
ejpam-3422	188	5	µ	µ	NOUN
ejpam-3422	188	6	in	in	ADP
ejpam-3422	188	7	a	a	DET
ejpam-3422	188	8	hyper	hyper	ADJ
ejpam-3422	188	9	gr	gr	NOUN
ejpam-3422	188	10	-	-	PUNCT
ejpam-3422	188	11	algebra	algebra	NOUN
ejpam-3422	188	12	h	h	NOUN
ejpam-3422	188	13	is	be	AUX
ejpam-3422	188	14	a	a	DET
ejpam-3422	188	15	fuzzy	fuzzy	ADJ
ejpam-3422	188	16	implicative	implicative	ADJ
ejpam-3422	188	17	hyper	hyper	ADJ
ejpam-3422	188	18	gr	gr	NOUN
ejpam-3422	188	19	-	-	PUNCT
ejpam-3422	188	20	ideal	ideal	NOUN
ejpam-3422	188	21	of	of	ADP
ejpam-3422	188	22	type	type	NOUN
ejpam-3422	188	23	2	2	NUM
ejpam-3422	188	24	,	,	PUNCT
ejpam-3422	188	25	then	then	ADV
ejpam-3422	188	26	µt	µt	PRON
ejpam-3422	188	27	is	be	AUX
ejpam-3422	188	28	an	an	DET
ejpam-3422	188	29	implicative	implicative	ADJ
ejpam-3422	188	30	hyper	hyper	ADJ
ejpam-3422	188	31	gr	gr	NOUN
ejpam-3422	188	32	-	-	PUNCT
ejpam-3422	188	33	ideal	ideal	NOUN
ejpam-3422	188	34	of	of	ADP
ejpam-3422	188	35	h	h	NOUN
ejpam-3422	189	1	whenever	whenever	SCONJ
ejpam-3422	189	2	µt	µt	PROPN
ejpam-3422	189	3	6=	6=	PROPN
ejpam-3422	189	4	φ	φ	PROPN
ejpam-3422	189	5	and	and	CCONJ
ejpam-3422	189	6	t	t	PROPN
ejpam-3422	189	7	∈	∈	PROPN
ejpam-3422	190	1	[	[	X
ejpam-3422	190	2	0	0	NUM
ejpam-3422	190	3	,	,	PUNCT
ejpam-3422	190	4	1	1	NUM
ejpam-3422	190	5	]	]	PUNCT
ejpam-3422	190	6	.	.	PUNCT
ejpam-3422	191	1	proof	proof	NOUN
ejpam-3422	191	2	.	.	PUNCT
ejpam-3422	192	1	suppose	suppose	VERB
ejpam-3422	192	2	µ	µ	PRON
ejpam-3422	192	3	is	be	AUX
ejpam-3422	192	4	a	a	DET
ejpam-3422	192	5	fuzzy	fuzzy	ADJ
ejpam-3422	192	6	implicative	implicative	ADJ
ejpam-3422	192	7	hyper	hyper	ADJ
ejpam-3422	192	8	gr	gr	NOUN
ejpam-3422	192	9	-	-	PUNCT
ejpam-3422	192	10	ideal	ideal	NOUN
ejpam-3422	192	11	of	of	ADP
ejpam-3422	192	12	type	type	NOUN
ejpam-3422	192	13	2	2	NUM
ejpam-3422	192	14	and	and	CCONJ
ejpam-3422	192	15	µt	µt	PRON
ejpam-3422	192	16	6=	6=	PROPN
ejpam-3422	192	17	φ	φ	PROPN
ejpam-3422	192	18	.	.	PUNCT
ejpam-3422	193	1	let	let	VERB
ejpam-3422	193	2	t	t	PROPN
ejpam-3422	193	3	∈	∈	PROPN
ejpam-3422	194	1	[	[	X
ejpam-3422	194	2	0	0	NUM
ejpam-3422	194	3	,	,	PUNCT
ejpam-3422	194	4	1	1	NUM
ejpam-3422	194	5	]	]	PUNCT
ejpam-3422	194	6	.	.	PUNCT
ejpam-3422	195	1	since	since	SCONJ
ejpam-3422	195	2	µt	µt	PROPN
ejpam-3422	195	3	6=	6=	PROPN
ejpam-3422	195	4	φ	φ	NUM
ejpam-3422	195	5	,	,	PUNCT
ejpam-3422	195	6	there	there	PRON
ejpam-3422	195	7	exist	exist	VERB
ejpam-3422	195	8	x	x	SYM
ejpam-3422	195	9	∈	∈	PROPN
ejpam-3422	195	10	µt	µt	PROPN
ejpam-3422	195	11	.	.	PUNCT
ejpam-3422	195	12	by	by	ADP
ejpam-3422	195	13	fim1	fim1	NOUN
ejpam-3422	195	14	,	,	PUNCT
ejpam-3422	195	15	µ(0	µ(0	NOUN
ejpam-3422	195	16	)	)	PUNCT
ejpam-3422	195	17	≥	≥	NOUN
ejpam-3422	195	18	µ(x	µ(x	NOUN
ejpam-3422	195	19	)	)	PUNCT
ejpam-3422	195	20	≥	≥	NOUN
ejpam-3422	195	21	t.	t.	NOUN
ejpam-3422	196	1	it	it	PRON
ejpam-3422	196	2	follows	follow	VERB
ejpam-3422	196	3	that	that	SCONJ
ejpam-3422	196	4	0	0	NUM
ejpam-3422	196	5	∈	∈	PROPN
ejpam-3422	196	6	µt	µt	PROPN
ejpam-3422	196	7	.	.	PUNCT
ejpam-3422	197	1	let	let	VERB
ejpam-3422	197	2	x	x	PRON
ejpam-3422	197	3	,	,	PUNCT
ejpam-3422	197	4	y	y	PROPN
ejpam-3422	197	5	,	,	PUNCT
ejpam-3422	197	6	z	z	PROPN
ejpam-3422	197	7	∈	∈	PROPN
ejpam-3422	197	8	h	h	NOUN
ejpam-3422	197	9	such	such	ADJ
ejpam-3422	197	10	that	that	SCONJ
ejpam-3422	197	11	(	(	PUNCT
ejpam-3422	197	12	x	x	X
ejpam-3422	197	13	~	~	PUNCT
ejpam-3422	197	14	z	z	X
ejpam-3422	197	15	)	)	PUNCT
ejpam-3422	197	16	~	~	PUNCT
ejpam-3422	197	17	(	(	PUNCT
ejpam-3422	197	18	y	y	X
ejpam-3422	197	19	~	~	PUNCT
ejpam-3422	197	20	x	x	X
ejpam-3422	197	21	)	)	PUNCT
ejpam-3422	198	1	⊆	⊆	NUM
ejpam-3422	198	2	µt	µt	NOUN
ejpam-3422	198	3	and	and	CCONJ
ejpam-3422	198	4	z	z	PROPN
ejpam-3422	198	5	∈	∈	PROPN
ejpam-3422	199	1	µt	µt	PROPN
ejpam-3422	199	2	.	.	PUNCT
ejpam-3422	199	3	then	then	ADV
ejpam-3422	199	4	for	for	ADP
ejpam-3422	199	5	any	any	DET
ejpam-3422	199	6	u	u	NOUN
ejpam-3422	199	7	∈	∈	PROPN
ejpam-3422	199	8	(	(	PUNCT
ejpam-3422	199	9	x	x	X
ejpam-3422	199	10	~	~	PUNCT
ejpam-3422	199	11	z	z	X
ejpam-3422	199	12	)	)	PUNCT
ejpam-3422	199	13	~	~	PUNCT
ejpam-3422	199	14	(	(	PUNCT
ejpam-3422	199	15	y	y	X
ejpam-3422	199	16	~	~	PUNCT
ejpam-3422	199	17	x	x	X
ejpam-3422	199	18	)	)	PUNCT
ejpam-3422	199	19	there	there	PRON
ejpam-3422	199	20	exist	exist	VERB
ejpam-3422	199	21	a	a	DET
ejpam-3422	199	22	∈	∈	NOUN
ejpam-3422	199	23	µt	µt	ADP
ejpam-3422	199	24	such	such	ADJ
ejpam-3422	199	25	that	that	SCONJ
ejpam-3422	199	26	u	u	PROPN
ejpam-3422	199	27	�	�	PROPN
ejpam-3422	199	28	a.	a.	NOUN
ejpam-3422	199	29	by	by	ADP
ejpam-3422	199	30	fim2	fim2	PROPN
ejpam-3422	199	31	,	,	PUNCT
ejpam-3422	199	32	µ(u	µ(u	PROPN
ejpam-3422	199	33	)	)	PUNCT
ejpam-3422	199	34	≥	≥	NOUN
ejpam-3422	199	35	µ(a	µ(a	NOUN
ejpam-3422	199	36	)	)	PUNCT
ejpam-3422	199	37	≥	≥	NOUN
ejpam-3422	199	38	t.	t.	NOUN
ejpam-3422	199	39	it	it	PRON
ejpam-3422	199	40	follows	follow	VERB
ejpam-3422	199	41	from	from	ADP
ejpam-3422	199	42	fim1	fim1	NOUN
ejpam-3422	199	43	that	that	SCONJ
ejpam-3422	199	44	µ(x	µ(x	VERB
ejpam-3422	199	45	)	)	PUNCT
ejpam-3422	199	46	≥	≥	NOUN
ejpam-3422	199	47	min	min	PROPN
ejpam-3422	199	48	{	{	PUNCT
ejpam-3422	199	49	inf	inf	NOUN
ejpam-3422	199	50	u∈(x	u∈(x	PROPN
ejpam-3422	199	51	~	~	SYM
ejpam-3422	199	52	z)~(y	z)~(y	PROPN
ejpam-3422	199	53	~	~	SYM
ejpam-3422	199	54	x	x	X
ejpam-3422	199	55	)	)	PUNCT
ejpam-3422	199	56	µ(u	µ(u	NOUN
ejpam-3422	199	57	)	)	PUNCT
ejpam-3422	199	58	,	,	PUNCT
ejpam-3422	199	59	µ(z	µ(z	PROPN
ejpam-3422	199	60	)	)	PUNCT
ejpam-3422	199	61	}	}	PUNCT
ejpam-3422	199	62	≥	≥	NOUN
ejpam-3422	199	63	min{t	min{t	PROPN
ejpam-3422	199	64	,	,	PUNCT
ejpam-3422	199	65	t	t	PROPN
ejpam-3422	199	66	}	}	PUNCT
ejpam-3422	199	67	=	=	SYM
ejpam-3422	199	68	t.	t.	NOUN
ejpam-3422	199	69	hence	hence	ADV
ejpam-3422	199	70	,	,	PUNCT
ejpam-3422	199	71	x	x	PUNCT
ejpam-3422	199	72	∈	∈	ADJ
ejpam-3422	199	73	µt	µt	X
ejpam-3422	199	74	and	and	CCONJ
ejpam-3422	199	75	so	so	ADV
ejpam-3422	199	76	µt	µt	PRON
ejpam-3422	199	77	is	be	AUX
ejpam-3422	199	78	implicative	implicative	ADJ
ejpam-3422	199	79	hyper	hyper	ADJ
ejpam-3422	199	80	gr	gr	NOUN
ejpam-3422	199	81	-	-	PUNCT
ejpam-3422	199	82	ideal	ideal	NOUN
ejpam-3422	199	83	of	of	ADP
ejpam-3422	199	84	h.	h.	PROPN
ejpam-3422	199	85	theorem	theorem	VERB
ejpam-3422	199	86	4.10	4.10	NUM
ejpam-3422	199	87	.	.	PUNCT
ejpam-3422	200	1	if	if	SCONJ
ejpam-3422	200	2	µ	µ	NOUN
ejpam-3422	200	3	is	be	AUX
ejpam-3422	200	4	a	a	DET
ejpam-3422	200	5	fuzzy	fuzzy	ADJ
ejpam-3422	200	6	implicative	implicative	ADJ
ejpam-3422	200	7	hyper	hyper	ADJ
ejpam-3422	200	8	gr	gr	NOUN
ejpam-3422	200	9	-	-	PUNCT
ejpam-3422	200	10	ideal	ideal	NOUN
ejpam-3422	200	11	of	of	ADP
ejpam-3422	200	12	type	type	NOUN
ejpam-3422	200	13	1	1	NUM
ejpam-3422	200	14	(	(	PUNCT
ejpam-3422	200	15	type	type	NOUN
ejpam-3422	200	16	2	2	NUM
ejpam-3422	200	17	)	)	PUNCT
ejpam-3422	200	18	in	in	ADP
ejpam-3422	200	19	h	h	NOUN
ejpam-3422	200	20	,	,	PUNCT
ejpam-3422	200	21	then	then	ADV
ejpam-3422	200	22	the	the	DET
ejpam-3422	200	23	set	set	NOUN
ejpam-3422	200	24	i	i	PRON
ejpam-3422	200	25	=	=	PUNCT
ejpam-3422	200	26	{	{	PUNCT
ejpam-3422	200	27	x	x	PUNCT
ejpam-3422	200	28	∈	∈	NOUN
ejpam-3422	200	29	h|µ(x	h|µ(x	NOUN
ejpam-3422	200	30	)	)	PUNCT
ejpam-3422	200	31	=	=	SYM
ejpam-3422	200	32	µ(0	µ(0	NOUN
ejpam-3422	200	33	)	)	PUNCT
ejpam-3422	200	34	}	}	PUNCT
ejpam-3422	200	35	is	be	AUX
ejpam-3422	200	36	an	an	DET
ejpam-3422	200	37	implicative	implicative	ADJ
ejpam-3422	200	38	hyper	hyper	ADJ
ejpam-3422	200	39	gr	gr	NOUN
ejpam-3422	200	40	-	-	PUNCT
ejpam-3422	200	41	ideal	ideal	NOUN
ejpam-3422	200	42	of	of	ADP
ejpam-3422	200	43	h.	h.	NOUN
ejpam-3422	200	44	proof	proof	NOUN
ejpam-3422	200	45	.	.	PUNCT
ejpam-3422	201	1	let	let	VERB
ejpam-3422	201	2	x	x	PRON
ejpam-3422	201	3	,	,	PUNCT
ejpam-3422	201	4	y	y	PROPN
ejpam-3422	201	5	,	,	PUNCT
ejpam-3422	201	6	z	z	PROPN
ejpam-3422	201	7	∈	∈	PROPN
ejpam-3422	201	8	h	h	NOUN
ejpam-3422	201	9	such	such	ADJ
ejpam-3422	201	10	that	that	SCONJ
ejpam-3422	201	11	(	(	PUNCT
ejpam-3422	201	12	x	x	X
ejpam-3422	201	13	~	~	PUNCT
ejpam-3422	201	14	z	z	X
ejpam-3422	201	15	)	)	PUNCT
ejpam-3422	201	16	~	~	PUNCT
ejpam-3422	201	17	(	(	PUNCT
ejpam-3422	201	18	y	y	X
ejpam-3422	201	19	~	~	PUNCT
ejpam-3422	201	20	x	x	X
ejpam-3422	201	21	)	)	PUNCT
ejpam-3422	202	1	⊂	⊂	PROPN
ejpam-3422	203	1	i	i	PRON
ejpam-3422	203	2	and	and	CCONJ
ejpam-3422	203	3	z	z	PROPN
ejpam-3422	203	4	∈	∈	PROPN
ejpam-3422	203	5	i.	i.	NOUN
ejpam-3422	203	6	then	then	ADV
ejpam-3422	203	7	µ(z	µ(z	PROPN
ejpam-3422	203	8	)	)	PUNCT
ejpam-3422	203	9	=	=	SYM
ejpam-3422	203	10	µ(0	µ(0	NOUN
ejpam-3422	203	11	)	)	PUNCT
ejpam-3422	203	12	and	and	CCONJ
ejpam-3422	203	13	µ(u	µ(u	NOUN
ejpam-3422	203	14	)	)	PUNCT
ejpam-3422	203	15	=	=	SYM
ejpam-3422	203	16	µ(0	µ(0	NOUN
ejpam-3422	203	17	)	)	PUNCT
ejpam-3422	203	18	for	for	ADP
ejpam-3422	203	19	each	each	DET
ejpam-3422	203	20	u	u	NOUN
ejpam-3422	203	21	∈	∈	PROPN
ejpam-3422	203	22	(	(	PUNCT
ejpam-3422	203	23	x	x	X
ejpam-3422	203	24	~	~	PUNCT
ejpam-3422	203	25	z	z	X
ejpam-3422	203	26	)	)	PUNCT
ejpam-3422	203	27	~	~	PUNCT
ejpam-3422	203	28	(	(	PUNCT
ejpam-3422	203	29	y	y	X
ejpam-3422	203	30	~	~	PUNCT
ejpam-3422	203	31	z	z	X
ejpam-3422	203	32	)	)	PUNCT
ejpam-3422	203	33	.	.	PUNCT
ejpam-3422	204	1	by	by	ADP
ejpam-3422	204	2	fim2	fim2	PROPN
ejpam-3422	204	3	,	,	PUNCT
ejpam-3422	204	4	µ(0	µ(0	PROPN
ejpam-3422	204	5	)	)	PUNCT
ejpam-3422	204	6	≥	≥	NOUN
ejpam-3422	204	7	µ(x	µ(x	NOUN
ejpam-3422	204	8	)	)	PUNCT
ejpam-3422	204	9	≥	≥	NOUN
ejpam-3422	204	10	min	min	PROPN
ejpam-3422	204	11	{	{	PUNCT
ejpam-3422	204	12	inf	inf	NOUN
ejpam-3422	204	13	u∈(x	u∈(x	PROPN
ejpam-3422	204	14	~	~	SYM
ejpam-3422	204	15	z)~(y	z)~(y	PROPN
ejpam-3422	204	16	~	~	SYM
ejpam-3422	204	17	x	x	X
ejpam-3422	204	18	)	)	PUNCT
ejpam-3422	204	19	µ(u	µ(u	NOUN
ejpam-3422	204	20	)	)	PUNCT
ejpam-3422	204	21	,	,	PUNCT
ejpam-3422	204	22	µ(z	µ(z	PROPN
ejpam-3422	204	23	)	)	PUNCT
ejpam-3422	204	24	}	}	PUNCT
ejpam-3422	204	25	=	=	PUNCT
ejpam-3422	204	26	µ(0	µ(0	NOUN
ejpam-3422	204	27	)	)	PUNCT
ejpam-3422	204	28	.	.	PUNCT
ejpam-3422	205	1	then	then	ADV
ejpam-3422	205	2	,	,	PUNCT
ejpam-3422	205	3	µ(x	µ(x	X
ejpam-3422	205	4	)	)	PUNCT
ejpam-3422	205	5	=	=	SYM
ejpam-3422	205	6	µ(0	µ(0	NOUN
ejpam-3422	205	7	)	)	PUNCT
ejpam-3422	205	8	and	and	CCONJ
ejpam-3422	205	9	so	so	ADV
ejpam-3422	205	10	x	x	SYM
ejpam-3422	205	11	∈	∈	PROPN
ejpam-3422	205	12	i.	i.	NOUN
ejpam-3422	205	13	thus	thus	ADV
ejpam-3422	205	14	,	,	PUNCT
ejpam-3422	205	15	i	i	PRON
ejpam-3422	205	16	is	be	AUX
ejpam-3422	205	17	fuzzy	fuzzy	ADJ
ejpam-3422	205	18	implicative	implicative	ADJ
ejpam-3422	205	19	hyper	hyper	ADJ
ejpam-3422	205	20	gr	gr	NOUN
ejpam-3422	205	21	-	-	PUNCT
ejpam-3422	205	22	ideal	ideal	NOUN
ejpam-3422	205	23	of	of	ADP
ejpam-3422	205	24	type	type	NOUN
ejpam-3422	205	25	1	1	NUM
ejpam-3422	205	26	(	(	PUNCT
ejpam-3422	205	27	type	type	NOUN
ejpam-3422	205	28	2	2	NUM
ejpam-3422	205	29	)	)	PUNCT
ejpam-3422	205	30	in	in	ADP
ejpam-3422	205	31	h.	h.	PROPN
ejpam-3422	205	32	references	reference	VERB
ejpam-3422	205	33	417	417	NUM
ejpam-3422	205	34	references	reference	NOUN
ejpam-3422	205	35	[	[	X
ejpam-3422	205	36	1	1	NUM
ejpam-3422	205	37	]	]	X
ejpam-3422	205	38	r	r	NOUN
ejpam-3422	205	39	borzooei	borzooei	PROPN
ejpam-3422	205	40	and	and	CCONJ
ejpam-3422	205	41	m	m	PROPN
ejpam-3422	205	42	bakhsi	bakhsi	NOUN
ejpam-3422	205	43	.	.	PUNCT
ejpam-3422	206	1	(	(	PUNCT
ejpam-3422	206	2	weak	weak	ADJ
ejpam-3422	206	3	)	)	PUNCT
ejpam-3422	206	4	implicative	implicative	ADJ
ejpam-3422	206	5	hyper	hyper	ADJ
ejpam-3422	206	6	bck	bck	NOUN
ejpam-3422	206	7	-	-	PUNCT
ejpam-3422	206	8	ideals	ideal	NOUN
ejpam-3422	206	9	.	.	PUNCT
ejpam-3422	207	1	quasigroups	quasigroup	NOUN
ejpam-3422	207	2	and	and	CCONJ
ejpam-3422	207	3	related	related	ADJ
ejpam-3422	207	4	systems	system	NOUN
ejpam-3422	207	5	,	,	PUNCT
ejpam-3422	207	6	12:13–28	12:13–28	NUM
ejpam-3422	207	7	,	,	PUNCT
ejpam-3422	207	8	2004	2004	NUM
ejpam-3422	207	9	.	.	PUNCT
ejpam-3422	208	1	[	[	X
ejpam-3422	208	2	2	2	NUM
ejpam-3422	208	3	]	]	X
ejpam-3422	208	4	r	r	NOUN
ejpam-3422	208	5	borzooei	borzooei	PROPN
ejpam-3422	208	6	and	and	CCONJ
ejpam-3422	208	7	y	y	PROPN
ejpam-3422	208	8	jun	jun	PROPN
ejpam-3422	208	9	.	.	PROPN
ejpam-3422	208	10	intuitionistic	intuitionistic	ADJ
ejpam-3422	208	11	fuzzy	fuzzy	ADJ
ejpam-3422	208	12	hyper	hyper	ADJ
ejpam-3422	208	13	bck	bck	NOUN
ejpam-3422	208	14	-	-	PUNCT
ejpam-3422	208	15	ideals	ideal	NOUN
ejpam-3422	208	16	of	of	ADP
ejpam-3422	208	17	hyper	hyper	NOUN
ejpam-3422	208	18	bckalgebras	bckalgebras	PROPN
ejpam-3422	208	19	.	.	PUNCT
ejpam-3422	208	20	iranian	iranian	PROPN
ejpam-3422	208	21	journal	journal	PROPN
ejpam-3422	208	22	of	of	ADP
ejpam-3422	208	23	fuzzy	fuzzy	ADJ
ejpam-3422	208	24	systems	system	NOUN
ejpam-3422	208	25	,	,	PUNCT
ejpam-3422	208	26	1(1):61–73	1(1):61–73	NUM
ejpam-3422	208	27	,	,	PUNCT
ejpam-3422	208	28	2004	2004	NUM
ejpam-3422	208	29	.	.	PUNCT
ejpam-3422	209	1	[	[	X
ejpam-3422	209	2	3	3	X
ejpam-3422	209	3	]	]	X
ejpam-3422	209	4	p	p	X
ejpam-3422	209	5	das	das	PROPN
ejpam-3422	209	6	.	.	PUNCT
ejpam-3422	209	7	fuzzy	fuzzy	ADJ
ejpam-3422	209	8	groups	group	NOUN
ejpam-3422	209	9	and	and	CCONJ
ejpam-3422	209	10	level	level	NOUN
ejpam-3422	209	11	subgroups	subgroup	NOUN
ejpam-3422	209	12	.	.	PUNCT
ejpam-3422	210	1	j.	j.	PROPN
ejpam-3422	210	2	math	math	PROPN
ejpam-3422	210	3	.	.	PUNCT
ejpam-3422	211	1	anal	anal	PROPN
ejpam-3422	211	2	.	.	PUNCT
ejpam-3422	212	1	appl	appl	PROPN
ejpam-3422	212	2	.	.	PROPN
ejpam-3422	213	1	,	,	PUNCT
ejpam-3422	213	2	67:549–564	67:549–564	PROPN
ejpam-3422	213	3	,	,	PUNCT
ejpam-3422	213	4	1979	1979	NUM
ejpam-3422	213	5	.	.	PUNCT
ejpam-3422	214	1	[	[	X
ejpam-3422	214	2	4	4	NUM
ejpam-3422	214	3	]	]	X
ejpam-3422	214	4	r	r	NOUN
ejpam-3422	214	5	indangan	indangan	NOUN
ejpam-3422	214	6	and	and	CCONJ
ejpam-3422	214	7	g	g	PROPN
ejpam-3422	214	8	petalcorin	petalcorin	NOUN
ejpam-3422	214	9	.	.	PUNCT
ejpam-3422	215	1	some	some	DET
ejpam-3422	215	2	results	result	NOUN
ejpam-3422	215	3	on	on	ADP
ejpam-3422	215	4	hyper	hyper	ADJ
ejpam-3422	215	5	gr	gr	NOUN
ejpam-3422	215	6	-	-	PUNCT
ejpam-3422	215	7	ideals	ideal	NOUN
ejpam-3422	215	8	of	of	ADP
ejpam-3422	215	9	a	a	DET
ejpam-3422	215	10	hyper	hyper	ADJ
ejpam-3422	215	11	gralgebra	gralgebra	NOUN
ejpam-3422	215	12	.	.	PUNCT
ejpam-3422	216	1	journal	journal	NOUN
ejpam-3422	216	2	of	of	ADP
ejpam-3422	216	3	algebra	algebra	PROPN
ejpam-3422	216	4	and	and	CCONJ
ejpam-3422	216	5	applied	apply	VERB
ejpam-3422	216	6	mathematics	mathematic	NOUN
ejpam-3422	216	7	,	,	PUNCT
ejpam-3422	216	8	14:101–119	14:101–119	NUM
ejpam-3422	216	9	,	,	PUNCT
ejpam-3422	216	10	2016	2016	NUM
ejpam-3422	216	11	.	.	PUNCT
ejpam-3422	217	1	[	[	X
ejpam-3422	217	2	5	5	NUM
ejpam-3422	217	3	]	]	PUNCT
ejpam-3422	217	4	r	r	NOUN
ejpam-3422	217	5	indangan	indangan	NOUN
ejpam-3422	217	6	,	,	PUNCT
ejpam-3422	217	7	g	g	NOUN
ejpam-3422	217	8	petalcorin	petalcorin	NOUN
ejpam-3422	217	9	,	,	PUNCT
ejpam-3422	217	10	and	and	CCONJ
ejpam-3422	217	11	a	a	DET
ejpam-3422	217	12	villa	villa	NOUN
ejpam-3422	217	13	.	.	PUNCT
ejpam-3422	218	1	some	some	DET
ejpam-3422	218	2	hyper	hyper	ADJ
ejpam-3422	218	3	homomorphic	homomorphic	ADJ
ejpam-3422	218	4	properties	property	NOUN
ejpam-3422	218	5	on	on	ADP
ejpam-3422	218	6	hyper	hyper	ADJ
ejpam-3422	218	7	gr	gr	NOUN
ejpam-3422	218	8	-	-	PUNCT
ejpam-3422	218	9	algebras	algebra	NOUN
ejpam-3422	218	10	.	.	PUNCT
ejpam-3422	218	11	journal	journal	PROPN
ejpam-3422	218	12	of	of	ADP
ejpam-3422	218	13	algebra	algebra	PROPN
ejpam-3422	218	14	and	and	CCONJ
ejpam-3422	218	15	applied	apply	VERB
ejpam-3422	218	16	mathematics	mathematic	NOUN
ejpam-3422	218	17	,	,	PUNCT
ejpam-3422	218	18	15:100–121	15:100–121	PROPN
ejpam-3422	218	19	,	,	PUNCT
ejpam-3422	218	20	2017	2017	NUM
ejpam-3422	218	21	.	.	PUNCT
ejpam-3422	219	1	[	[	X
ejpam-3422	219	2	6	6	NUM
ejpam-3422	219	3	]	]	X
ejpam-3422	219	4	y	y	PROPN
ejpam-3422	219	5	jun	jun	PROPN
ejpam-3422	219	6	and	and	CCONJ
ejpam-3422	219	7	x	x	SYM
ejpam-3422	219	8	long	long	ADV
ejpam-3422	219	9	.	.	PUNCT
ejpam-3422	220	1	fuzzy	fuzzy	ADJ
ejpam-3422	220	2	hyper	hyper	ADJ
ejpam-3422	220	3	bck	bck	NOUN
ejpam-3422	220	4	-	-	PUNCT
ejpam-3422	220	5	ideals	ideal	NOUN
ejpam-3422	220	6	of	of	ADP
ejpam-3422	220	7	hyper	hyper	ADJ
ejpam-3422	220	8	bck	bck	NOUN
ejpam-3422	220	9	-	-	PUNCT
ejpam-3422	220	10	algebras	algebras	PROPN
ejpam-3422	220	11	.	.	PUNCT
ejpam-3422	221	1	scientiae	scientiae	PROPN
ejpam-3422	221	2	mathematics	mathematics	PROPN
ejpam-3422	221	3	japonicae	japonicae	PROPN
ejpam-3422	221	4	online	online	ADV
ejpam-3422	221	5	,	,	PUNCT
ejpam-3422	221	6	4:415–422	4:415–422	NOUN
ejpam-3422	221	7	,	,	PUNCT
ejpam-3422	221	8	2001	2001	NUM
ejpam-3422	221	9	.	.	PUNCT
ejpam-3422	222	1	[	[	X
ejpam-3422	222	2	7	7	X
ejpam-3422	222	3	]	]	X
ejpam-3422	222	4	y	y	PROPN
ejpam-3422	222	5	jun	jun	PROPN
ejpam-3422	222	6	and	and	CCONJ
ejpam-3422	222	7	w	w	NOUN
ejpam-3422	222	8	shim	shim	NOUN
ejpam-3422	222	9	.	.	PUNCT
ejpam-3422	223	1	fuzzy	fuzzy	ADJ
ejpam-3422	223	2	implicative	implicative	ADJ
ejpam-3422	223	3	hyper	hyper	ADJ
ejpam-3422	223	4	bck	bck	NOUN
ejpam-3422	223	5	-	-	PUNCT
ejpam-3422	223	6	ideals	ideal	NOUN
ejpam-3422	223	7	of	of	ADP
ejpam-3422	223	8	hyper	hyper	ADJ
ejpam-3422	223	9	bck	bck	NOUN
ejpam-3422	223	10	-	-	PUNCT
ejpam-3422	223	11	algebras	algebras	PROPN
ejpam-3422	223	12	.	.	PUNCT
ejpam-3422	224	1	international	international	ADJ
ejpam-3422	224	2	journal	journal	PROPN
ejpam-3422	224	3	of	of	ADP
ejpam-3422	224	4	mathematics	mathematics	PROPN
ejpam-3422	224	5	and	and	CCONJ
ejpam-3422	224	6	mathematical	mathematical	ADJ
ejpam-3422	224	7	sciences	science	NOUN
ejpam-3422	224	8	,	,	PUNCT
ejpam-3422	224	9	29(2):63–70	29(2):63–70	NUM
ejpam-3422	224	10	,	,	PUNCT
ejpam-3422	224	11	2002	2002	NUM
ejpam-3422	224	12	.	.	PUNCT
ejpam-3422	225	1	[	[	X
ejpam-3422	225	2	8	8	NUM
ejpam-3422	225	3	]	]	X
ejpam-3422	225	4	y	y	PROPN
ejpam-3422	225	5	jun	jun	PROPN
ejpam-3422	225	6	,	,	PUNCT
ejpam-3422	225	7	m	m	PROPN
ejpam-3422	225	8	zahedi	zahedi	PROPN
ejpam-3422	225	9	,	,	PUNCT
ejpam-3422	225	10	x	x	X
ejpam-3422	225	11	xin	xin	PROPN
ejpam-3422	225	12	,	,	PUNCT
ejpam-3422	225	13	and	and	CCONJ
ejpam-3422	225	14	r	r	NOUN
ejpam-3422	225	15	borzoei	borzoei	NOUN
ejpam-3422	225	16	.	.	PUNCT
ejpam-3422	226	1	on	on	ADP
ejpam-3422	226	2	hyper	hyper	ADJ
ejpam-3422	226	3	bck	bck	NOUN
ejpam-3422	226	4	-	-	PUNCT
ejpam-3422	226	5	algebras	algebras	PROPN
ejpam-3422	226	6	.	.	PUNCT
ejpam-3422	227	1	italian	italian	ADJ
ejpam-3422	227	2	j.	j.	PROPN
ejpam-3422	227	3	pure	pure	PROPN
ejpam-3422	227	4	appl	appl	PROPN
ejpam-3422	227	5	.	.	PUNCT
ejpam-3422	227	6	math	math	PROPN
ejpam-3422	227	7	.	.	PUNCT
ejpam-3422	227	8	,	,	PUNCT
ejpam-3422	227	9	8:127–136	8:127–136	NUM
ejpam-3422	227	10	,	,	PUNCT
ejpam-3422	227	11	2000	2000	NUM
ejpam-3422	227	12	.	.	PUNCT
ejpam-3422	228	1	[	[	X
ejpam-3422	228	2	9	9	NUM
ejpam-3422	228	3	]	]	X
ejpam-3422	228	4	m	m	PROPN
ejpam-3422	228	5	kang	kang	PROPN
ejpam-3422	228	6	.	.	PUNCT
ejpam-3422	228	7	hyper	hyper	PROPN
ejpam-3422	229	1	k	k	PROPN
ejpam-3422	229	2	-	-	PUNCT
ejpam-3422	229	3	subalgebras	subalgebras	PROPN
ejpam-3422	229	4	based	base	VERB
ejpam-3422	229	5	on	on	ADP
ejpam-3422	229	6	fuzzy	fuzzy	ADJ
ejpam-3422	229	7	points	point	NOUN
ejpam-3422	229	8	.	.	PUNCT
ejpam-3422	230	1	communications	communication	NOUN
ejpam-3422	230	2	of	of	ADP
ejpam-3422	230	3	the	the	DET
ejpam-3422	230	4	korean	korean	ADJ
ejpam-3422	230	5	mathematical	mathematical	ADJ
ejpam-3422	230	6	society	society	NOUN
ejpam-3422	230	7	,	,	PUNCT
ejpam-3422	230	8	26(3):385–403	26(3):385–403	NOUN
ejpam-3422	230	9	,	,	PUNCT
ejpam-3422	230	10	2011	2011	NUM
ejpam-3422	230	11	.	.	PUNCT
ejpam-3422	231	1	[	[	X
ejpam-3422	231	2	10	10	NUM
ejpam-3422	231	3	]	]	X
ejpam-3422	231	4	x	x	X
ejpam-3422	231	5	long	long	ADV
ejpam-3422	231	6	.	.	PUNCT
ejpam-3422	232	1	hyper	hyper	ADJ
ejpam-3422	232	2	bci	bci	NOUN
ejpam-3422	232	3	-	-	PUNCT
ejpam-3422	232	4	algebras	algebras	X
ejpam-3422	232	5	.	.	PUNCT
ejpam-3422	233	1	discuss	discuss	PROPN
ejpam-3422	233	2	math	math	NOUN
ejpam-3422	233	3	.	.	PUNCT
ejpam-3422	234	1	soc	soc	PROPN
ejpam-3422	234	2	.	.	PUNCT
ejpam-3422	234	3	,	,	PUNCT
ejpam-3422	234	4	26:5–19	26:5–19	NUM
ejpam-3422	234	5	,	,	PUNCT
ejpam-3422	234	6	2006	2006	NUM
ejpam-3422	234	7	.	.	PUNCT
ejpam-3422	235	1	[	[	X
ejpam-3422	235	2	11	11	NUM
ejpam-3422	235	3	]	]	X
ejpam-3422	235	4	f	f	PROPN
ejpam-3422	235	5	marty	marty	PROPN
ejpam-3422	235	6	.	.	PUNCT
ejpam-3422	236	1	sur	sur	PROPN
ejpam-3422	236	2	une	une	PROPN
ejpam-3422	236	3	generalization	generalization	PROPN
ejpam-3422	236	4	de	de	X
ejpam-3422	236	5	la	la	PROPN
ejpam-3422	236	6	notion	notion	NOUN
ejpam-3422	236	7	de	de	PROPN
ejpam-3422	236	8	group	group	NOUN
ejpam-3422	236	9	.	.	PUNCT
ejpam-3422	237	1	8th	8th	ADJ
ejpam-3422	237	2	congress	congress	PROPN
ejpam-3422	237	3	math	math	NOUN
ejpam-3422	237	4	.	.	PUNCT
ejpam-3422	238	1	scandenaves	scandenave	NOUN
ejpam-3422	238	2	(	(	PUNCT
ejpam-3422	238	3	stockholm	stockholm	PROPN
ejpam-3422	238	4	)	)	PUNCT
ejpam-3422	238	5	,	,	PUNCT
ejpam-3422	238	6	pages	page	NOUN
ejpam-3422	238	7	45–49	45–49	NUM
ejpam-3422	238	8	,	,	PUNCT
ejpam-3422	238	9	1934	1934	NUM
ejpam-3422	238	10	.	.	PUNCT
ejpam-3422	239	1	[	[	X
ejpam-3422	239	2	12	12	NUM
ejpam-3422	239	3	]	]	X
ejpam-3422	239	4	f	f	X
ejpam-3422	239	5	nisar	nisar	PROPN
ejpam-3422	239	6	,	,	PUNCT
ejpam-3422	239	7	r	r	NOUN
ejpam-3422	239	8	tariq	tariq	NOUN
ejpam-3422	239	9	,	,	PUNCT
ejpam-3422	239	10	and	and	CCONJ
ejpam-3422	239	11	s	s	AUX
ejpam-3422	239	12	bhatti	bhatti	NOUN
ejpam-3422	239	13	.	.	PUNCT
ejpam-3422	240	1	bi	bi	ADJ
ejpam-3422	240	2	-	-	ADJ
ejpam-3422	240	3	polar	polar	ADV
ejpam-3422	240	4	-	-	PUNCT
ejpam-3422	240	5	valued	value	VERB
ejpam-3422	240	6	fuzzy	fuzzy	ADJ
ejpam-3422	240	7	hyper	hyper	ADJ
ejpam-3422	240	8	subalgebras	subalgebra	NOUN
ejpam-3422	240	9	of	of	ADP
ejpam-3422	240	10	a	a	DET
ejpam-3422	240	11	hyper	hyper	ADJ
ejpam-3422	240	12	bci	bci	NOUN
ejpam-3422	240	13	-	-	NOUN
ejpam-3422	240	14	algebra	algebra	NOUN
ejpam-3422	240	15	.	.	PUNCT
ejpam-3422	241	1	world	world	NOUN
ejpam-3422	241	2	applied	apply	VERB
ejpam-3422	241	3	sciences	science	NOUN
ejpam-3422	241	4	journal	journal	NOUN
ejpam-3422	241	5	,	,	PUNCT
ejpam-3422	241	6	9(1):25–33	9(1):25–33	NUM
ejpam-3422	241	7	,	,	PUNCT
ejpam-3422	241	8	2010	2010	NUM
ejpam-3422	241	9	.	.	PUNCT
ejpam-3422	242	1	[	[	X
ejpam-3422	242	2	13	13	NUM
ejpam-3422	242	3	]	]	X
ejpam-3422	242	4	f	f	X
ejpam-3422	242	5	nisar	nisar	PROPN
ejpam-3422	242	6	,	,	PUNCT
ejpam-3422	242	7	r	r	NOUN
ejpam-3422	242	8	tariq	tariq	NOUN
ejpam-3422	242	9	,	,	PUNCT
ejpam-3422	242	10	and	and	CCONJ
ejpam-3422	242	11	s	s	AUX
ejpam-3422	242	12	bhatti	bhatti	NOUN
ejpam-3422	242	13	.	.	PUNCT
ejpam-3422	242	14	fuzzy	fuzzy	ADJ
ejpam-3422	242	15	ideals	ideal	NOUN
ejpam-3422	242	16	in	in	ADP
ejpam-3422	242	17	hyper	hyper	ADJ
ejpam-3422	242	18	bci	bci	NOUN
ejpam-3422	242	19	-	-	PUNCT
ejpam-3422	242	20	algebras	algebra	NOUN
ejpam-3422	242	21	.	.	PUNCT
ejpam-3422	243	1	world	world	PROPN
ejpam-3422	243	2	applied	apply	VERB
ejpam-3422	243	3	sciences	science	NOUN
ejpam-3422	243	4	journal	journal	NOUN
ejpam-3422	243	5	,	,	PUNCT
ejpam-3422	243	6	16(12):1771–1777	16(12):1771–1777	PROPN
ejpam-3422	243	7	,	,	PUNCT
ejpam-3422	243	8	2012	2012	NUM
ejpam-3422	243	9	.	.	PUNCT
ejpam-3422	244	1	[	[	X
ejpam-3422	244	2	14	14	NUM
ejpam-3422	244	3	]	]	PUNCT
ejpam-3422	244	4	n	n	DET
ejpam-3422	244	5	palaniappan	palaniappan	NOUN
ejpam-3422	244	6	,	,	PUNCT
ejpam-3422	244	7	p	p	NOUN
ejpam-3422	244	8	veerappan	veerappan	NOUN
ejpam-3422	244	9	,	,	PUNCT
ejpam-3422	244	10	and	and	CCONJ
ejpam-3422	244	11	r	r	NOUN
ejpam-3422	244	12	devi	devi	PROPN
ejpam-3422	244	13	.	.	PUNCT
ejpam-3422	245	1	intuitionistic	intuitionistic	ADJ
ejpam-3422	245	2	fuzzy	fuzzy	ADJ
ejpam-3422	245	3	ideals	ideal	NOUN
ejpam-3422	245	4	in	in	ADP
ejpam-3422	245	5	hyper	hyper	ADJ
ejpam-3422	245	6	bcialgebras	bcialgebra	NOUN
ejpam-3422	245	7	.	.	PUNCT
ejpam-3422	246	1	international	international	ADJ
ejpam-3422	246	2	journal	journal	PROPN
ejpam-3422	246	3	of	of	ADP
ejpam-3422	246	4	computational	computational	ADJ
ejpam-3422	246	5	science	science	NOUN
ejpam-3422	246	6	and	and	CCONJ
ejpam-3422	246	7	mathematics	mathematic	NOUN
ejpam-3422	246	8	,	,	PUNCT
ejpam-3422	246	9	4(3):271	4(3):271	NUM
ejpam-3422	246	10	–	–	PUNCT
ejpam-3422	246	11	285	285	NUM
ejpam-3422	246	12	,	,	PUNCT
ejpam-3422	246	13	2012	2012	NUM
ejpam-3422	246	14	.	.	PUNCT
ejpam-3422	247	1	[	[	X
ejpam-3422	247	2	15	15	NUM
ejpam-3422	247	3	]	]	X
ejpam-3422	247	4	h	h	NOUN
ejpam-3422	247	5	singh	singh	PROPN
ejpam-3422	247	6	,	,	PUNCT
ejpam-3422	247	7	m	m	PROPN
ejpam-3422	247	8	gupta	gupta	PROPN
ejpam-3422	247	9	,	,	PUNCT
ejpam-3422	247	10	t	t	PROPN
ejpam-3422	247	11	meitzler	meitzler	NOUN
ejpam-3422	247	12	,	,	PUNCT
ejpam-3422	247	13	z	z	PROPN
ejpam-3422	247	14	hou	hou	PROPN
ejpam-3422	247	15	,	,	PUNCT
ejpam-3422	247	16	k	k	PROPN
ejpam-3422	247	17	garg	garg	PROPN
ejpam-3422	247	18	,	,	PUNCT
ejpam-3422	247	19	a	a	DET
ejpam-3422	247	20	solo	solo	NOUN
ejpam-3422	247	21	,	,	PUNCT
ejpam-3422	247	22	and	and	CCONJ
ejpam-3422	247	23	l	l	PROPN
ejpam-3422	247	24	zadeh	zadeh	PROPN
ejpam-3422	247	25	.	.	PUNCT
ejpam-3422	248	1	real	real	ADJ
ejpam-3422	248	2	-	-	PUNCT
ejpam-3422	248	3	life	life	NOUN
ejpam-3422	248	4	applications	application	NOUN
ejpam-3422	248	5	of	of	ADP
ejpam-3422	248	6	fuzzy	fuzzy	ADJ
ejpam-3422	248	7	logic	logic	NOUN
ejpam-3422	248	8	.	.	PUNCT
ejpam-3422	249	1	hindawi	hindawi	ADJ
ejpam-3422	249	2	publishing	publishing	NOUN
ejpam-3422	249	3	corporation	corporation	NOUN
ejpam-3422	249	4	advances	advance	VERB
ejpam-3422	249	5	in	in	ADP
ejpam-3422	249	6	fuzzy	fuzzy	ADJ
ejpam-3422	249	7	systems	system	NOUN
ejpam-3422	249	8	volume	volume	NOUN
ejpam-3422	249	9	,	,	PUNCT
ejpam-3422	249	10	2013:271–285	2013:271–285	NUM
ejpam-3422	249	11	,	,	PUNCT
ejpam-3422	249	12	2013	2013	NUM
ejpam-3422	249	13	.	.	PUNCT
ejpam-3422	250	1	[	[	X
ejpam-3422	250	2	16	16	NUM
ejpam-3422	250	3	]	]	SYM
ejpam-3422	250	4	g	g	NOUN
ejpam-3422	250	5	tabaranza	tabaranza	NOUN
ejpam-3422	250	6	and	and	CCONJ
ejpam-3422	250	7	j	j	PROPN
ejpam-3422	250	8	vilela	vilela	NOUN
ejpam-3422	250	9	.	.	PUNCT
ejpam-3422	251	1	on	on	ADP
ejpam-3422	251	2	fuzzy	fuzzy	ADJ
ejpam-3422	251	3	hyper	hyper	ADJ
ejpam-3422	251	4	b	b	NOUN
ejpam-3422	251	5	-	-	PUNCT
ejpam-3422	251	6	ideals	ideal	NOUN
ejpam-3422	251	7	of	of	ADP
ejpam-3422	251	8	hyper	hyper	ADJ
ejpam-3422	251	9	b	b	NOUN
ejpam-3422	251	10	-	-	PUNCT
ejpam-3422	251	11	algebras	algebras	PROPN
ejpam-3422	251	12	.	.	PUNCT
ejpam-3422	251	13	international	international	ADJ
ejpam-3422	251	14	journal	journal	PROPN
ejpam-3422	251	15	of	of	ADP
ejpam-3422	251	16	algebra	algebra	PROPN
ejpam-3422	251	17	,	,	PUNCT
ejpam-3422	251	18	12(5):197–209	12(5):197–209	NOUN
ejpam-3422	251	19	,	,	PUNCT
ejpam-3422	251	20	2018	2018	NUM
ejpam-3422	251	21	.	.	PUNCT
ejpam-3422	252	1	[	[	X
ejpam-3422	252	2	17	17	NUM
ejpam-3422	252	3	]	]	X
ejpam-3422	252	4	l	l	PROPN
ejpam-3422	252	5	zadeh	zadeh	PROPN
ejpam-3422	252	6	.	.	PUNCT
ejpam-3422	252	7	fuzzy	fuzzy	ADJ
ejpam-3422	252	8	sets	set	NOUN
ejpam-3422	252	9	.	.	PUNCT
ejpam-3422	253	1	information	information	NOUN
ejpam-3422	253	2	and	and	CCONJ
ejpam-3422	253	3	control	control	NOUN
ejpam-3422	253	4	,	,	PUNCT
ejpam-3422	253	5	8:338–353	8:338–353	NUM
ejpam-3422	253	6	,	,	PUNCT
ejpam-3422	253	7	1965	1965	NUM
ejpam-3422	253	8	.	.	PUNCT